Optical waveguide structures

ABSTRACT

The purely bound electromagnetic modes of propagation supported by waveguide structures comprised of a thin lossy metal film of finite width embedded in an infinite homogeneous dielectric have been characterized at optical wavelengths. One of the fundamental modes supported by the structure exhibits very interesting characteristics and is potentially quite useful. It evolves with decreasing film thickness and width towards the TEM wave supported by the background (an evolution similar to that exhibited by the s b  mode in symmetric metal film slab waveguides), its losses and phase constant tending asymptotically towards those of the TEM wave. Attenuation values can be well below those of the s b  mode supported by the corresponding metal film slab waveguide. Low mode power attenuation in the neighborhood of 10 to 0.1 dB/cm is achievable at optical communications wavelengths, with even lower values being possible. Carefully selecting the film&#39;s thickness and width can make this mode the only long-ranging one supported. In addition, the mode can have a field distribution that renders it excitable using an end-fire approach. The existence of this mode renders the finite-width metal film waveguide attractive for applications requiring short propagation distances and 2-D field confinement in the transverse plane, enabling various devices to be constructed, such as couplers, splitters, modulators, interferometers, switches and periodic structures. Under certain conditions, an asymmetric structure can support a long-ranging mode having a field distribution that is suitable to excitation using an end-fire technique. Like asymmetric slab waveguides. The attenuation of the long-ranging mode near cutoff decreases very rapidly, much more so than the attenuation related to the long-ranging mode in a similar symmetric structure. The cutoff thickness of a long-ranging mode in an asymmetric finite-width structure is larger than the cutoff thickness of the s b  mode in a similar asymmetric slab waveguide. This implies that the long-ranging mode supported by an asymmetric finite-width structure is more sensitive to the asymmetry in the structure compared to the s b  mode supported by a similar slab waveguide. This result is interesting and potentially useful in that the propagation of such a mode can be affected by a smaller change in the dielectric constant of the substrate or superstrate compared with similar slab structures.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a Continuation-in-Part of U.S. patent application Ser. No.09/742,422 filed Dec. 22, 2000, now U.S. Pat. No. 6,614,960, whichitself was a Continuation-in-Part of U.S. patent application Ser. No.09/629,816 filed Jul. 31, 2000, now U.S. Pat. No. 6,442,321 issued Aug.27, 2002, and which claimed priority from U.S. Provisional patentapplication No. 60/171,606 filed Dec. 23, 1999, Canadian patentapplication No. 2,314,723 filed Jul. 31, 2000 and Canadian patentapplication No. 2,319,949 filed Sep. 20, 2000. The contents of theseapplications are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Technical Field

The invention relates to optical devices and is especially applicable towaveguide structures and integrated optics.

2. Background Art

This specification refers to several published articles. Forconvenience, the articles are cited in full in a numbered list at theend of the description and cited by number in the specification itself.The contents of these articles are incorporated herein by reference andthe reader is directed to them for reference.

In the context of this patent specification, the term “opticalradiation” embraces electromagnetic waves having wavelengths in theinfrared, visible and ultraviolet ranges.

The terms “finite” and “infinite” as used herein are used by personsskilled in this art to distinguish between waveguides having “finite”widths in which the actual width is significant to the performance ofthe waveguide and the physics governing its operation and so-called“infinite” waveguides where the width is so great that it has nosignificant effect upon the performance and physics or operation.

At optical wavelengths, the electromagnetic properties of some metalsclosely resemble those of an electron gas, or equivalently of a coldplasma. Metals that resemble an almost ideal plasma are commonly termed“noble metals” and include, among others, gold, silver and copper.Numerous experiments as well as classical electron theory both yield anequivalent negative dielectric constant for many metals when excited byan electromagnetic wave at or near optical wavelengths [1,2]. In arecent experimental study, the dielectric function of silver has beenaccurately measured over the visible optical spectrum and a very closecorrelation between the measured dielectric function and that obtainedvia the electron gas model has been demonstrated [3].

It is well-known that the interface between semi-infinite materialshaving positive and negative dielectric constants can guide TM(Transverse Magnetic) surface waves. In the case of a metal-dielectricinterface at optical wavelengths, these waves are termedplasmon-polariton modes and propagate as electromagnetic fields coupledto surface plasmons (surface plasma oscillations) comprised ofconduction electrons in the metal [4].

It is known to use a metal film of a certain thickness bounded bydielectrics above and below as an optical slab (planar, infinitely wide)waveguiding structure, with the core of the waveguide being the metalfilm. When the film is thin enough, the plasmon-polariton modes guidedby the interfaces become coupled due to field tunnelling through themetal, thus creating supermodes that exhibit dispersion with metalthickness. The modes supported by infinitely wide symmetric andasymmetric metal film structures are well-known, as these structureshave been studied by numerous researchers; some notable published worksinclude references [4] to [10].

In general, only two purely bound TM modes, each having three fieldcomponents, are guided by an infinitely wide metal film waveguide. Inthe plane perpendicular to the direction of wave propagation, theelectric field of the modes is comprised of a single component, normalto the interfaces and having either a symmetric or asymmetric spatialdistribution across the waveguide. Consequently, these modes are denoteds_(b) and a_(b) modes, respectively. The s_(b) mode can have a smallattenuation constant and is often termed a long-range surfaceplasmon-polariton. The fields related to the a_(b) mode penetratefurther into the metal than in the case of the s_(b) mode and can bemuch lossier by comparison. Interest in the modes supported by thinmetal films has recently intensified due to their useful application inoptical communications devices and components. Metal films are commonlyemployed in optical polarizing devices [11] while long-range surfaceplasmon-polaritons can be used for signal transmission [7]. In additionto purely bound modes, leaky modes are also known to be supported bythese structures.

Infinitely wide metal film structures, however, are of limited practicalinterest since they offer one-dimensional (1-D) field confinement only,with confinement occurring along the vertical axis perpendicular to thedirection of wave propagation, implying that modes will spread outlaterally as they propagate from a point source used as the excitation.Metal films of finite width have recently been proposed in connectionwith polarizing devices [12], but merely as a cladding.

In addition to the lack of lateral confinement, plasmon-polariton wavesguided by a metal-dielectric interface are in general quite lossy. Evenlong-range surface plasmons guided by a metal film can be lossy bycomparison with dielectric waveguides. Known devices exploit this highloss associated with surface plasmons for the construction ofplasmon-polariton based modulators and switches. Generally, knownplasmon-polariton based modulator and switch devices can be classifiedalong two distinct architectures. The first architecture is based on thephenomenon of attenuated total reflection (ATR) and the secondarchitecture is based on mode coupling between a dielectric waveguideand a nearby metal. Both architectures depend on the dissipation ofoptical power within an interacting metal structure.

ATR based devices depend on the coupling of an optical beam; which isincident upon a dielectric-metal structure placed in optical proximity,to a surface plasmon-polariton mode supported by the metal structure. Ata specific angle of incidence, which depends on the materials used andthe particular geometry of the device, coupling to a plasmon mode ismaximised and a drop in the power reflected from the metal surface isobserved. ATR based modulators make use of this attenuated reflectionphenomenon along with means for varying electrically or otherwise atleast one of the optical parameters of one of the dielectrics boundingthe metal structure in order to shift the angle of incidence wheremaximum coupling to plasmons occurs. Electrically shifting the angle ofmaximum coupling results in a modulation of the intensity of thereflected light. Examples of devices that are based on this architectureare disclosed in references [23] to [36].

Mode coupling devices are based on the optical coupling of lightpropagating in a dielectric waveguide to a nearby metal film placed acertain distance away and in parallel with the dielectric waveguide. Thecoupling coefficient between the optical mode propagating in thewaveguide and the plasmon-polariton mode supported by the nearby metalfilm is adjusted via the materials selected and the geometricalparameters of the device. Means is provided for varying, electrically orotherwise, at least one of the optical parameters of one of thedielectrics bounding the metal. Varying an optical parameter (the indexof refraction, say) varies the coupling coefficient between the opticalwave propagating in the dielectric waveguide and the lossyplasmon-polariton wave supported by the metal. This results in amodulation in the intensity of the light exiting the dielectricwaveguide. References [37] to [40] disclose various deviceimplementations based upon this phenomenon. Reference [41] furtherdiscusses the physical phenomenon underlying the operation of thesedevices.

Reference [42] discusses an application of the ATR phenomenon forrealising an optical switch or bistable device.

These known modulation and switching devices disadvantageously requirerelative high control voltages and have limited electrical/opticalbandwidth.

SUMMARY OF THE INVENTION

The present invention seeks to eliminate, or at least mitigate, one ormore of the disadvantages of the prior art, or at least provide analternative.

According to one aspect of the present invention there is provided anoptical device comprising a waveguide structure formed by a thin stripof material having a relatively high free charge carrier densitysurrounded by material having a relatively low free charge carrierdensity, the strip having finite width and thickness with dimensionssuch that optical radiation having a free space wavelength in the rangefrom about 0.81 μm to about 2 μm couples to the strip and propagatesalong the length of the strip as a plasmon-polariton wave.

Such a strip of finite width offers two-dimensional (2-D) confinement inthe transverse plane, i.e. perpendicular to the direction ofpropagation, and, since suitable low-loss waveguides can be fabricatedfrom such strip, it may be useful for signal transmission and routing orto construct components such as couplers, power splitters,interferometers, modulators, switches and other typical components ofintegrated optics. In such devices, different sections of the stripserving different functions, in some cases in combination withadditional electrodes. The strip sections may be discrete andconcatenated or otherwise interrelated, or sections of one or morecontinuous strips.

For example, where the optical radiation has a free-space wavelength of1550 nm, and the waveguide is made of a strip of a noble metalsurrounded by a good dielectric, say glass, suitable dimensions for thestrip are thickness less than about 0.1 microns, preferably about 20 nm,and width of a few microns, preferably about 4 microns.

The strip could be straight, curved, bent, tapered, and so on.

The dielectric material may be inhomogeneous, for example a combinationof slabs, strips, laminae, and so on. The conductive or semiconductivestrip may be inhomogeneous, for example a layer of gold and a layer oftitanium.

The plasmon-polariton wave which propagates along the structure may beexcited by an appropriate optical field incident at one of the ends ofthe waveguide, as in an end-fire configuration, and/or by a differentradiation coupling means.

The device may further comprise means for varying the value of anelectromagnetic property of at least a portion of said surroundingmaterial so as to vary the propagation characteristics of the waveguidestructure and the propagation of the plasmon-polariton wave.

In some embodiments of the invention, for one said value of theelectromagnetic property, propagation of the plasmon-polariton wave issupported and, for another value of said electromagnetic property,propagation of the plasmon-polariton wave is at least inhibited. Suchembodiments may comprise modulators or switches.

Different embodiments of the invention may employ different means ofvarying the electromagnetic property, such as varying the size of atleast one of said portions, especially if it comprises a fluid.

The at least one variable electromagnetic property of the material maycomprise permittivity, permeability or conductivity.

Various objects, features, aspects and advantages of the presentinvention will become more apparent from the following detaileddescription, taken in conjunction with the accompanying drawings, ofpreferred embodiments of the invention which are described by way ofexample only.

BRIEF DESCRIPTION OF DRAWINGS

FIGS. 1(a) and 1(b) are a cross-sectional illustration and a plan view,respectively, of a symmetric waveguide structure embodying the presentinvention in which the core is comprised of a lossy metal film ofthickness t, width w, length l and permittivity ε₂ embedded in acladding or background comprising an “infinite” homogeneous dielectrichaving a permittivity ε₁;

FIGS. 2(a) and 2(b) illustrate dispersion characteristics with thicknessof the first eight modes supported by a symmetric metal film waveguideof width w=1 μm. The a_(b) and s_(b) modes supported for the case w=∞are shown for comparison. (a) Normalized phase constant; (b) Normalizedattenuation constant;

FIGS. 3(a), (b), (c), (d), (e) and (f) illustrate the spatialdistribution of the six field components related to the ss_(b) ⁰ modesupported by a symmetric metal film waveguide of thickness t=100 nm andwidth w=1 μm. The waveguide cross-section is located in the x-y planeand the metal is bounded by the region −0.5≦×≦0.5 μm and −0.05≦y≦0.05μm, outlined as the rectangular dashed contour. The field distributionsare normalized such that max|Re{E_(y)}|=1;

FIGS. 4(a), (b), (c), (d), (e) and (f) illustrate the spatialdistribution of the six field components related to the sa_(b) ⁰ modesupported by a symmetric metal film waveguide of thickness t=100 nm andwidth w=1 μm. The waveguide cross-section is located in the x-y planeand the metal is bounded by the region −0.5≦×≦0.5 μm and −0.05≦y≦0.05μm, outlined as the rectangular dashed contour. The field distributionsare normalized such that max|Re{E_(y)}|=1;

FIGS. 5(a), (b), (c), (d), (e) and (f) illustrate the spatialdistribution of the six field components related to the as_(b) ⁰ modesupported by a symmetric metal film waveguide of thickness t=100 nm andwidth w=1 μm. The waveguide cross-section is located in the x-y planeand the metal is bounded by the region −0.5≦×≦0.5 μm and −0.05≦y≦0.05μm, outlined as the rectangular dashed contour. The field distributionsare normalized such that max|Re{E_(y)}|=1;

FIGS. 6(a), (b), (c), (d), (e) and (f) illustrate the spatialdistribution of the six field components related to the aa_(b) ⁰ modesupported by a symmetric metal film waveguide of thickness t=100 nm andwidth w=1 μm. The waveguide cross-section is located in the x-y planeand the metal is bounded by the region −0.5≦×≦0.5 μm and −0.05≦y≦0.05μm, outlined as the rectangular dashed contour. The field distributionsare normalized such that max|Re{E_(y)}|=1;

FIGS. 7(a), (b), (c), (d), (e) and (f) are contour plots of Re{S_(z)}associated with the ss_(b) ⁰ mode for symmetric metal film waveguides ofwidth w=1 μm and various thicknesses. The power confinement factor cf isalso given in all cases, and is computed via equation (12) with the areaof the waveguide core A, taken as the area of the metal region. In allcases, the outline of the metal film is shown as the rectangular dashedcontour;

FIG. 8 illustrates a normalized profile of Re{S_(z)} associated with thess_(b) ⁰ mode for a symmetric metal film waveguide of width w=1 μm andthickness t=20 nm. The waveguide cross-section is located in the x-yplane and the metal film is bounded by the region −0.5≦×≦0.5 μm and−0.01≦y≦0.01 μm, outlined as the rectangular dashed contour;

FIGS. 9(a), (b), (c) and (d) illustrate the spatial distribution of theE_(y) field component related to some higher order modes supported by asymmetric metal film waveguide of thickness t=100 nm and width w=1 μm.In all cases, the waveguide cross-section is located in the x-y planeand the metal film is bounded by the region −0.5≦×≦0.5 μm and−0.05≦y≦0.05 μm, outlined as the rectangular dashed contour;

FIGS. 10(a) and (b) illustrate dispersion characteristics with thicknessof the first six modes supported by a symmetric metal film waveguide ofwidth w=0.5 μm. The a_(b) and s_(b) modes supported for the case w=∞ areshown for comparison. (a) Normalized phase constant; (b) Normalizedattenuation constant;

FIGS. 11(a) and (b) illustrate dispersion characteristics with thicknessof the ss_(b) ⁰ mode supported by symmetric metal film waveguides ofvarious widths. The s_(b) mode supported for the case w=∞ is shown forcomparison. (a) Normalized phase constant; (b) Normalized attenuationconstant;

FIGS. 12(a), (b), (c) and (d) illustrate a contour plot of Re{S_(z)}associated with the ss_(b) ⁰ mode for symmetric metal film waveguides ofthickness t=20 nm and various widths. The power confinement factor cf isalso given in all cases, and is computed via equation (12) with the areaof the waveguide core A_(c) taken as the area of the metal region. Inall cases, the outline of the metal film is shown as the rectangulardashed contour;

FIG. 13 illustrates dispersion characteristics with thickness of thess_(b) ⁰ mode supported by a symmetric metal film waveguide of widthw=0.5 μm for various background permittivities ε_(r,1). The normalizedphase constant is plotted on the left axis and the normalizedattenuation constant is plotted on the right one;

FIGS. 14(a), (b), (c) and (d) illustrates a contour plot of Re{Sz}associated with the ss_(b) ⁰ mode for a symmetric metal film waveguideof width w=0.5 μm and thickness t=20 nm for various backgroundpermittivities ε_(r,1). In all cases, the outline of the metal film isshown as the rectangular dashed contour;

FIGS. 15(a) and (b) illustrate dispersion characteristics with frequencyof the ss_(b) ⁰ mode supported by symmetric metal film waveguides ofwidth w=0.5 μm and w=1 μm and various thicknesses t. The s_(b) modesupported for the case w=∞ and the thicknesses considered is shown forcomparison. (a) Normalized phase constant. (b) Mode power attenuationcomputed using Equation (16) and scaled to dB/cm;

FIGS. 16(a), (b), (c), (d), (e) and (f) illustrate a contour plot ofRe{S_(z)} associated with the ss_(b) ⁰ mode for symmetric metal filmwaveguides of width w=0.5 μm and w=1 μm, and thickness t=20 nm atvarious free-space wavelengths of excitation λ₀. In all cases, theoutline of the metal film is shown as the rectangular dashed contour;

FIGS. 17(a) and 17(b) are a cross-sectional view and a plan view,respectively, of a second embodiment of the invention in the form of anasymmetric waveguide structure formed by a core comprising a lossy metalfilm of thickness t, width w and permittivity ε₂ supported by ahomogeneous semi-infinite substrate of permittivity ε₁ and with a coveror superstrate comprising a homogeneous semi-infinite dielectric ofpermittivity ε₃;

FIGS. 18(a) and 18(b) illustrate dispersion characteristics withthickness of the first seven modes supported by an asymmetric metal filmwaveguide of width w=1 μm. The a_(b) and s_(b) modes supported for thecase w=∞ are shown for comparison. (a) Normalized phase constant. (b)Normalized attenuation constant;

FIGS. 19(a), (b), (c) and (d) illustrate spatial distribution of theE_(y) field component related to the ss_(b) ⁰ mode supported by anasymmetric metal film waveguide of width w=1 μm for four filmthicknesses. The waveguide cross-section is located in the x-y plane andthe metal region is outlined as the rectangular dashed contour. Thefield distributions are normalized such that max|{E_(y)}|=1;

FIGS. 20(a), (b), (c) and (d) illustrate spatial distribution of theE_(y) field component related to two higher order modes supported by anasymmetric metal film waveguide of width w=1 μm for two filmthicknesses. In all cases, the waveguide cross-section is located in thex-y plane and the metal region is outlined as the rectangular dashedcontour. The field distributions are normalized such thatmax|{E_(y)}|=1;

FIGS. 21(a) and (b) illustrate dispersion characteristics with thicknessof the first six modes supported by an asymmetric metal film waveguideof width w=1 μm. The a_(b) and s_(b) modes supported for the case w=∞are shown for comparison. (a) Normalized phase constant. (b) Normalizedattenuation constant;

FIGS. 22(a), (b), (c) and (d) illustrate spatial distribution of theE_(y) field component related to modes supported by an asymmetric metalfilm waveguide of width w=1 μm. In all cases, the waveguidecross-section is located in the x-y plane and the metal region isoutlined as the rectangular dashed contour. The field distributions arenormalized such that max|{E_(y)}|=1;

FIGS. 23(a) and 23(b) illustrate dispersion characteristics withthickness of the first six modes supported by an asymmetric metal filmwaveguide of width w=0.5 μm. The a_(b) and s_(b) modes supported for thecase w=∞ are shown for comparison. (a) Normalized phase constant. (b)Normalized attenuation constant;

FIGS. 24(a) and 24(b) illustrate dispersion characteristics withthickness of the ss_(b) ⁰ and sa_(b) ¹ modes supported by an asymmetricmetal film waveguide of width w=0.5 μm for various cases of ε₃. (a)Normalized phase constant; the inset shows an enlarged view of theregion bounded by 0.04≦t≦0.08 μm and 2.0≦β/β₀≦2.3. (b) Normalizedattenuation constant; the inset shows an enlarged view of the regionbounded by 0.05≦t≦0.08 μm and 7.0×10⁻³≦α/β₀≦2.0×10⁻²;

FIGS. 25(a), (b), (c) and (d) illustrate spatial distribution of theE_(y) field component related to the sa_(b) ¹ mode supported by anasymmetric metal film waveguide of width w=0.5 μm for four filmthicknesses. The waveguide cross-section is located in the x-y plane andthe metal region is outlined as the rectangular dashed contour. Thefield distributions are normalized such that max|{E_(y)}|=1;

FIGS. 26(a), (b), (c) and (d) illustrate a contour plot of {S_(z)}associated with the long-ranging modes supported by asymmetric metalfilm waveguides of width w=0.5 μm and having different superstratepermittivities ε₃. In all cases, the outline of the metal film is shownas the rectangular dashed contour;

FIG. 27 is a plan view of a waveguide with opposite sides stepped toprovide different widths;

FIG. 28 is a plan view of a waveguide which is tapered and slanted;

FIG. 29 is a plan view of a trapezoidal waveguide;

FIG. 30 is a plan view of a waveguide having curved side edges andsuitable for use as a transition piece;

FIG. 31 is a plan view of a curved waveguide section suitable forinterconnecting waveguides at a corner;

FIG. 32 is a plan view of a two-way splitter/combiner formed by acombination of three straight waveguide sections and one taperedwaveguide section;

FIG. 33(a) is a plan view of an angled junction using a slanted section;

FIG. 33(b) is a plan view of an offset junction using an S-bend;

FIG. 34(a) is a plan view of a power divider formed by a trapezoidalsection and pairs of concatenated bends;

FIG. 34(b) is a plan view of a power divider similar to that shown inFIG. 34(a) but with a transition section formed by mirroring andoverlapping curved sections;

FIG. 35 is a plan view of a Mach-Zender interferometer formed using acombination of the waveguide sections;

FIG. 36(a) is a schematic plan view of a modulator using the Mach-Zenderwaveguide structure of FIG. 35;

FIGS. 36(b) and 36(c) are inset diagrams illustrating alternative waysof applying a modulation control voltage;

FIG. 37 is a plan view of a modulator using the Mach-Zender waveguidestructure of FIG. 35 and illustrating magnetic field control;

FIG. 38 is a plan view of a periodic structure formed by a series ofunit cells each comprising two waveguide sections having differentwidths and lengths;

FIG. 39 is a plan view of a periodic waveguide structure formed by aseries of unit cells each comprising two opposed trapezoidal waveguidesections;

FIG. 40(a) is a plan view of an edge coupler formed by two parallelstrips of straight waveguide with various other waveguides for couplingsignals to and from them;

FIG. 40(b) is an inset diagram illustrating a way of applying amodulation control voltage;

FIG. 40(c) is a plan view of an edge coupler similar to that shown inFIG. 40(a) but using S-bends;

FIG. 41(a) is a perspective view of an edge coupler in which theparallel strips are not co-planar;

FIG. 41(b) is an inset diagram illustrating a way of applying amodulation control voltage;

FIG. 42 is a plan view of an intersection formed by four sections ofwaveguide;

FIGS. 43(a) and 43(b) are a schematic front view and corresponding topplan view of an electro-optic modulator employing the waveguidestructure of FIG. 17(a);

FIGS. 44(a) and 44(b) are a schematic front view and corresponding topview of an alternative electro-optic modulator also using the waveguidestructure of FIG. 17(a);

FIG. 44(c) illustrates an alternative connection arrangement of themodulator of FIG. 44(a);

FIG. 45 is a schematic front view of a third embodiment of electro-opticmodulator also using the waveguide structure of FIG. 17(a);

FIG. 46 is a schematic front view of a magneto-optic modulator alsousing the waveguide structure of FIG. 17(a);

FIG. 47 is a schematic front view of a thermo-optic modulator also usingthe waveguide structure of FIG. 17(a);

FIG. 48 is a schematic perspective view of an electro-optic switch alsousing the waveguide structure of FIG. 17(a);

FIG. 49 is a schematic perspective view of a magneto-optic switch alsousing the waveguide structure of FIG. 17(a);

FIG. 50 is a schematic perspective view of a thermo-optic switch alsousing the waveguide structure of FIG. 17(a);

FIG. 51 gives the mode power attenuation for metal film waveguides ofvarious widths and thicknesses. The metal used is Au and the backgrounddielectric is SiO₂. The optical free-space wavelength of analysis is setto λ₀=1.55 μm; and

FIG. 52 gives the mode power attenuation for metal film waveguides ofvarious widths and thicknesses. The metal used is Al and the backgrounddielectric is SiO₂. The optical free-space wavelength of analysis is setto λ₀=1.55 μm.

DESCRIPTION OF THE PREFERRED EMBODIMENT

I. Introduction

In order to facilitate an understanding of the specific optical devicesembodying the invention, their theoretical basis will first be explainedwith reference to FIGS. 1 to 26(d).

The following is a comprehensive description of the purely bound modesof propagation supported by symmetric and asymmetric waveguidestructures comprised of a thin lossy metal film of finite-width as thecore. The core can be embedded in an “infinite” homogeneous dielectricmedium as shown in FIG. 1(a) or supported by a semi-infinite homogeneousdielectric substrate and covered by a different semi-infinitehomogeneous dielectric superstrate as shown in FIG. 17(a). Thedescription is organized as follows. Section II summarizes the physicalbasis and numerical technique used to analyze the structures ofinterest. Sections III through-VI describe the modes supported bysymmetric structures as shown in FIG. 1(a) and sections VII through Xdescribe the modes supported by asymmetric structures as shown in FIG.17(a). Concluding remarks are given in section XI.

II. Physical Basis and Numerical Technique

A symmetric structure embodying the present invention is shown in FIGS.1(a) and 1(b). It comprises a lossy metal film of thickness t, width wand equivalent permittivity ε₂, surrounded by a cladding or backgroundcomprising an infinite homogeneous dielectric of permittivity ε₁. FIG.17(a) shows an asymmetric structure (ε₁≠ε₃) embodying the presentinvention. The Cartesian coordinate axes used for the analysis are alsoshown with propagation taking place along the z axis, which is out ofthe page.

It is assumed that the metal region shown in FIGS. 1(a) and 17(a) can bemodelled as an electron gas over the wavelengths of interest. Accordingto classical or Drude electron theory, the complex relative permittivityof the metal region is given by the well-known plasma frequencydispersion relation [4]: $\begin{matrix}{ɛ_{r,2} = {\left( {1 - \frac{\omega_{p}^{2}}{\omega^{2} + v^{2}}} \right) - {j\left( \frac{\omega_{p}^{2}v}{\omega\left( {\omega^{2} + v^{2}} \right.} \right)}}} & (1)\end{matrix}$

where ω is the excitation frequency, ω_(p) is the electron plasmafrequency and ν is the effective electron collision frequency, oftenexpressed as ν=1/τ with τ defined as the relaxation time of electrons inthe metal. When ω²+ν²<ω_(p) ² (which is the case for many metals atoptical wavelengths) a negative value for the real part ε_(r,2) isobtained, implying that plasmon-polariton modes can be supported atinterfaces with normal dielectrics.

Electromagnetic Wave and Field Equations

The modes supported by the structures are obtained by solving a suitablydefined boundary value problem based on Maxwell's equations written inthe frequency domain for a lossy inhomogeneous isotropic medium.Uncoupling Maxwell's equations yields the following time-harmonicvectorial wave equations for the E and H fields:

∇×∇×E−ω ²ε(x,y)μE=0  (2)

∇×ε(x,y)⁻¹ ∇×H−ω ² μH=0  (3)

where the permittivity ε is a complex function of cross-sectional space,and describes the waveguide structure. For the structures analyzed inthis description, μ is homogeneous and taken as the permeability of freespace μ₀.

Due to the nature of the numerical method used to solve the boundaryvalue problem, the implicit y dependence of the permittivity can beimmediately removed since any inhomogeneity along y is treated bydividing the structure into a number of layers that are homogeneousalong this direction, and suitable boundary conditions are appliedbetween them.

The two vectorial wave equations (2) and (3) are expanded in each layerinto scalar wave equations, some being coupled by virtue of theremaining inhomogeneity in ε along x. Since the structure underconsideration is invariant along the propagation axis (taken to be inthe +z direction), the mode fields vary along this dimension accordingto e^(−γz) where γ=α+jβ is the complex propagation constant of the mode,α being its attenuation constant and β its phase constant. Substitutingthis field dependency into the scalar wave equations, and writing themfor TE^(x)(E_(x)=0) and TM^(x)(H_(x)=0) modes while making use of∇·[ε(x)E]=0 and ∇·H=0 accordingly, yields simplified and uncoupledscalar wave equations that are readily solved. The E_(y) component ofthe TE^(x) modes must satisfy the Helmholtz wave equation:$\begin{matrix}{{{\frac{\partial^{2}}{\partial x^{2}}E_{y}^{TE}} + {\frac{\partial^{2}}{\partial y^{2}}E_{y}^{TE}} + {\left\lbrack {\gamma^{2} + {\omega^{2}\mu \quad {\varepsilon (x)}}} \right\rbrack E_{y}^{TE}}} = 0} & (4)\end{matrix}$

and the H_(y) component of the TM^(x) modes must satisfy theSturm-Liouville wave equation: $\begin{matrix}{{{{\varepsilon (x)}{\frac{\partial}{\partial x}\left\lbrack {\frac{1}{\varepsilon (x)}\frac{\partial}{\partial x}H_{y}^{TM}} \right\rbrack}} + {\frac{\partial^{2}}{\partial y^{2}}H_{y}^{TM}} + {\left\lbrack {\gamma^{2} = {\omega^{2}\mu \quad {\varepsilon (x)}}} \right\rbrack H_{y}^{TM}}} = 0} & (5)\end{matrix}$

The superposition of the TE^(x) and TM^(x) mode families then describesany mode propagating in the structure analyzed. The electric andmagnetic field components resulting from this superposition are given bythe following equations: $\begin{matrix}{E_{x} = {\frac{- 1}{j\quad \omega \quad \gamma}\left\lbrack {{\frac{\partial}{\partial x}\left( {\frac{1}{\varepsilon (x)}\frac{\partial}{\partial x}H_{y}^{TM}} \right)} + {\omega^{2}\mu \quad H_{y}^{TM}}} \right\rbrack}} & (6) \\{E_{y} = {E_{y}^{TE} - {\frac{}{j\quad \omega \quad \gamma \quad {\varepsilon (x)}}\frac{\partial^{2}}{{\partial x}{\partial y}}H_{y}^{TM}}}} & (7) \\{E_{z} = {{\frac{1}{\gamma}\frac{\partial}{\partial y}E_{y}^{TE}} + {\frac{1}{j\quad \omega \quad {\varepsilon (x)}}\frac{\partial}{\partial x}H_{y}^{TM}}}} & (8) \\{H_{x} = {\frac{1}{j\quad \omega \quad \gamma}\left\lbrack {{\frac{1}{\mu}\frac{\partial^{2}}{\partial x^{2}}E_{y}^{TE}} + {\omega^{2}{\varepsilon (x)}E_{y}^{TE}}} \right\rbrack}} & (9) \\{H_{y} = {{\frac{1}{j\quad \omega \quad \gamma \quad \mu}\frac{\partial^{2}}{{\partial x}{\partial y}}E_{y}^{TE}} + H_{y}^{TM}}} & (10) \\{H_{z} = {{{- \frac{1}{j\quad \omega \quad \mu}}\frac{\partial}{\partial x}E_{y}^{TE}} + {\frac{1}{\gamma}\frac{\partial}{\partial y}H_{y}^{TM}}}} & (11)\end{matrix}$

In order to obtain a mode of propagation supported by a waveguidingstructure, the Helmholtz and Sturm-Liouville wave equations (4) and (5),along with the field equations (6)-(11), must be solved for thepropagation constant γ using appropriate boundary conditions appliedbetween layers and at the horizontal and vertical limits.

Poynting Vector and Power Confinement Factor

The power confinement factor is defined as the ratio of mode complexpower carried through a portion of a waveguide's cross-section withrespect to the mode complex power carried through the entire waveguidecross-section. Formally it is expressed as: $\begin{matrix}{{cf} = \frac{{\int{\int_{A_{c}}{S_{z}{s}}}}}{{\int{\int_{A_{\infty}}{s_{z}{s}}}}}} & (12)\end{matrix}$

where A_(c) is usually taken as the area of the waveguide core and A_(∞)implies integration over the entire waveguide cross-section (which canbe all cross-sectional space for an open structure) or the entirecross-sectional computational domain. S_(z) refers to the z component ofthe Poynting vector: $\begin{matrix}{S_{z} = {\frac{1}{2}\left( {{E_{x}H_{y}^{*}} - {E_{y}H_{x}^{*}}} \right)}} & (13)\end{matrix}$

and H*_(x,y) denotes the complex conjugate of H_(x,y). The spatialdistribution of a component of the Poynting vector is easily computedfrom the spatial distribution of the relevant electric and magnetic modefield components.

Numerical Solution Approach

The boundary value problem governed by equations (4) to (11) is solvedby applying the Method of Lines (MoL). The MoL is a well-known numericaltechnique and its application to various electromagnetic problems,including optical waveguiding, is well-established [14]. The MoL isrigorous, accurate and flexible. It can handle a wide variety ofwaveguide geometries, including the structures at hand. The method isnot known to generate spurious or non-physical modes. The MoLformulation used herein is based on the formulation reported in [15],but simplified for isotropic media, as prescribed by equations (4)-(11)and reported in [16]. Except for a 1-D spatial discretization, themethod is exact.

The main idea behind the MoL is that the differential field equationsgoverning a waveguiding problem are discretized only as far as necessaryso that generalized analytic solutions can be applied to derive ahomogeneous matrix problem describing all modes supported by thestructure. This approach renders the method accurate and computationallyefficient since only −1 dimensions must be discretized to solve an Ndimension problem. In the case of a two-dimensional (2-D) waveguidingstructure, this means that only one spatial dimension needs to bediscretized. The main features of this procedure, as applied to a modalanalysis problem, are described below.

The x axis and the function ε(x) are discretized using two shiftednon-equidistant line systems, parallel to the y axis.

The differential operators ∂\∂x and ∂²/∂²x in the wave and fieldequations are replaced by finite difference approximations that includethe lateral boundary conditions.

The discretized wave equations are diagonalized using appropriatetransformations matrices.

The diagonalization procedure yields in the transform domain two systemsof uncoupled one-dimensional (1-D) differential equations along theremaining dimension (in this case along the y axis).

These differential equations are solved analytically and tangentialfield matching conditions are applied at interfaces between layers alongwith the top and bottom boundary conditions.

The last field matching condition, applied near the center of thestructure, yields a homogeneous matrix equation of the form G(γ){tildeover (e)}=0 which operates on transformed tangential fields.

The complex propagation constant γ of modes is then obtained bysearching for values that satisfy det[G(γ)]=0.

Once the propagation constant of a mode has been determined, the spatialdistribution of all six field components of the mode are easilygenerated.

A mode power confinement factor can be computed by first computing thespatial distribution of S_(z) which is then integrated according toEquation (12).

The open structures shown in FIGS. 1(a) and 17(a) are discretized alongthe x axis and the generalized analytic solution applied along the yaxis. The physical symmetry of the structures is exploited to increasethe accuracy of the results and to reduce the numerical effort requiredto generate the mode solutions. For the symmetric structure shown inFIG. 1(a), this is achieved by placing either electric wall (E_(tan)=0)or magnetic wall (H_(tan)=0) boundary conditions along the x and y axes.For the asymmetric structure shown in FIG. 17(a), this is achieved byplacing electric wall or magnetic wall boundary conditions along the yaxis only. The remaining horizontal boundary conditions are placed atinfinity and the remaining lateral boundary condition is either placedfar enough from the guide to have a negligible effect on the modecalculation, or a lateral absorbing boundary condition is used tosimulate infinite space, depending on the level of confinement observedin the resulting mode. The use of numerical methods to solvedifferential equations inevitably raises questions regarding theconvergence of computed results and their accuracy. The propagationconstant of a mode computed using the method of lines converges in amonotonic or smooth manner with a reduction in the discretizationinterval (which increases the number of lines in the calculation andthus the numerical effort). This suggests that extrapolation can be usedto generate a more accurate value for the propagation constant, and thisvalue can then be used to compute the error in values obtained using thecoarser discretizations [17]. This anticipated error does not correspondto the actual error in the propagation constant as the latter could onlybe known if the analytic or exact value were available. The anticipatederror, however, still provides a useful measure of accuracy since itmust tend toward zero as more accurate results are generated.

The convergence of the computed propagation constant of the modessupported by the structures of interest has been monitored during theentire study. The anticipated error in the results presented herein isestimated as 1% on average and 6% in the worst case. These error valuesare based on extrapolated propagation constants computed usingRichardson's extrapolation formula [18].

III. Mode Characteristics and Evolution With Film Thickness: SymmetricStructures

A. Review of Mode Solutions for Metal Film Slab Waveguides

The review begins with the reproduction of results for an infinitelywide symmetric metal film waveguide, as shown in FIG. 1(a) with w=∞,taken from the standard work on such structures [6]. In order to remainconsistent with their results, the optical free-space wavelength ofexcitation is set to λ₀=0.633 μm and their value for the relativepermittivity of the silver film at this wavelength is used:ε_(r,2)=−19−j0.53. The relative permittivity of the top and bottomdielectric regions is set to ε_(r,1)=4.

An infinitely wide structure supports only two purely bound TM(E_(x)=H_(y)=H_(z)=0) modes having transverse field components E_(y) andH_(x) that exhibit asymmetry or symmetry with respect to the x axis.These modes are created from the coupling of individualplasmon-polariton modes supported by the top and bottom interfaces andthey exhibit dispersion with film thickness. The widely acceptednomenclature for identifying them consists in using the letters a or sfor asymmetric or symmetric transverse field distributions,respectively, followed by a subscript b or l for bound or leaky modes,respectively. The propagation constants of the a_(b) and s_(b) modeshave been computed as a function of film thickness and the normalizedphase and attenuation constants are plotted in FIGS. 2(a) and 2(b),respectively.

From FIGS. 2(a) and 2(b), it is observed that the a_(b) and s_(b) modesbecome degenerate with increasing film thickness. As the separationbetween the top and bottom interfaces increases, the a_(b) and s_(b)modes begin to split into a pair of uncoupled plasmon-polariton modeslocalized at the metal-dielectric interfaces. The propagation constantsof the a_(b) and s_(b) modes thus tend towards that of aplasmon-polariton mode supported by the interface between semi-infinitemetallic and dielectric regions, which is given via the followingequations [6]: $\begin{matrix}{{\beta/\beta_{0}} = {{- {Re}}\left\{ \sqrt{\frac{\varepsilon_{r,1}\varepsilon_{r,2}}{\varepsilon_{r,1} + \varepsilon_{r,2}}} \right\}}} & (14) \\{{\alpha/\beta_{0}} = {{- {Im}}\left\{ \sqrt{\frac{\varepsilon_{r,1}\varepsilon_{r,2}}{\varepsilon_{r,1} + \varepsilon_{r,2}}} \right\}}} & (15)\end{matrix}$

where β₀=ω/c₀ with c₀ being the velocity of light in free space, andε_(r,1) and ε_(r,2) are the complex relative permittivities of thematerials used. Using the above equations, values of β/β₀=2.250646 andα/β₀=0.836247×10⁻² are obtained for ε_(r,1)=4 and ε_(r,2)=−19−j0.53.

As the thickness of the film decreases, the phase and attenuationconstants of the a_(b) mode increase, becoming very large for very thinfilms. This is due to the fact that the fields of this mode penetrateprogressively deeper into the metal as its thickness is reduced. In thecase of the s_(b) mode, a decreasing film thickness causes the oppositeeffect, that is, the fields penetrate progressively more into the topand bottom dielectric regions and less into the metal. The propagationconstant of this mode thus tends asymptotically towards that of a TEM(Transverse ElectroMagnetic) wave propagating in an infinite mediumhaving the same permittivity as the top and bottom dielectric regions.In this case, the attenuation constant decreases asymptotically towardszero since losses were neglected in these regions. The a_(b) and s_(b)modes do not have a cutoff thickness.

The fields in an infinitely wide structure do not exhibit any spatialvariation along x. Due to the nature of the MoL, and to the fact thatthe generalized analytical solution is applied along the y dimension,our results do not contain discretization errors and thus are in perfectagreement with those reported in [6].

B. Modes Supported by a Metal Film of Width w=1 μm

Next, the analysis of the structure shown in FIG. 1(a) for the case w=1μm will be explained. The material parameters and free-space wavelengththat were used in the previous case (w=∞) were also used here. The MoLwas applied and the discretization adjusted until convergence of thepropagation constant was observed. The physical quarter-symmetry of thestructure was exploited by placing vertical and horizontal electric ormagnetic walls along the y and x axes, respectively, which leads to fourpossible wall combinations as listed in Table 1. The first two purelybound (non-leaky) modes for each wall combination were found and theirdispersion with metal thickness computed. The results for these eightmodes are shown in FIGS. 2(a) and 2(b).

TABLE 1 Vertical-Horizontal wall combinations used along the axes ofsymmetry and proposed mode nomenclature: ew—electric wall, mw—magneticwall. V-H Walls Mode ew-ew as_(b) ^(m) mw-ew ss_(b) ^(m) mw-mw sa_(b)^(m) ew-mw aa_(b) ^(m)

Unlike its slab counterpart, pure TM modes are not supported by a metalfilm of finite width: all six field components are present in all modes.For a symmetric structure having an aspect ratio w/t>1, the Ey fieldcomponent dominates. The E_(x) field component increases in magnitudewith increasing film thickness and if w/t<1, then E_(x) dominates. It isproposed to identify the modes supported by a metal film of finitewidth, by extending the nomenclature used for metal film slabwaveguides. First a pair of letters being a or s identify whether themain transverse electric field component is asymmetric or symmetric withrespect to the y and x axes, respectively (in most practical structuresw/t>>1 and E_(y) is the main transverse electric field component). Asuperscript is then used to track the number of extrema observed in thespatial distribution of this field component along the largest dimension(usually along the x axis) between the corners. A second superscript ncould be added to track the extrema along the other dimension (the yaxis) if modes exhibiting them are found. Finally, a subscript b or l isused to identify whether the mode is bound or leaky. Leaky modes areknown to exist in metal film slab structures and though a search forthem has not been made at this time, their existence is anticipated.Table 1 relates the proposed mode nomenclature to the correspondingvertical and horizontal wall combinations used along the axes ofsymmetry.

The ss_(b) ⁰, sa_(b) ⁰, as_(b) ⁰ and aa_(b) ⁰ modes are the first modesgenerated (one for each of the four possible quarter-symmetries listedin Table 1, and having the largest phase constant) and thus may beconsidered as the fundamental modes supported by the structure. FIGS. 3to 6 show the field distributions of these modes over the cross-sectionof the waveguide for a metal film of thickness t=100 nm. As is observedfrom these figures, the main transverse electric field component is theE_(y) component and the symmetries in the spatial distribution of thiscomponent are reflected in the mode nomenclature. The outline of themetal is clearly seen in the distribution of the E_(y) component on allof these plots. As is observed from the figures, very little fieldtunnels through the metal to couple parallel edges for this case of filmthickness and width (very little coupling through the metal between thetop and bottom edges and between the left and right edges), thoughcoupling does occur along all edges between adjacent corners (mostlyalong the left and right ones), and also between perpendicular edgesthrough the corner.

FIGS. 2(a) and 2(b) suggests that the dispersion curves for these firstfour modes converge with increasing film thickness toward thepropagation constant of a plasmon-polariton mode supported by anisolated corner (though pairs of corners in this case remain weaklycoupled along the top and bottom edges due to the finite width of thefilm, even if its thickness goes to infinity). If both the filmthickness and width were to increase further, the four fundamental modeswould approach degeneracy with their propagation constant tendingtowards that of a plasmon-polariton mode supported by an isolatedcorner, and their mode fields becoming more localized near the cornersof the structure with maxima occurring at all four corners and fieldsdecaying in an exponential-like manner in all directions away from thecorners. This is further supported by considering the evolution of thefield distributions given in FIGS. 3 to 6 as both the thickness andwidth increase.

As the thickness of the film decreases, coupling between the top andbottom edges increases and the four modes split into a pair as the upperbranch (modes sa_(b) ⁰ and aa_(b) ⁰ which have a dominant E_(y) fieldcomponent exhibiting asymmetry with respect to the x axis) and a pair asthe lower branch (modes ss_(b) ⁰ and as_(b) ⁰ which have a dominantE_(y) field component exhibiting symmetry with respect to the x axis),as shown in FIGS. 2(a) and 2(b). The pair on the upper branch remainapproximately degenerate for all film thicknesses, though decreasing thefilm width would eventually break this degeneracy. The upper branchmodes do not change in character as the film thickness decreases. Theirfield distributions remain essentially unchanged from those shown inFIGS. 4 and 6 with the exception that confinement to the metal region isincreased thus causing an increase in their attenuation constant. Thisfield behaviour is consistent with that of the a_(b) mode supported by ametal film slab waveguide.

The modes on the lower branch begin to split at a film thickness ofabout 80 nm, as shown in FIGS. 2(a) and 2(b). As the film thicknessdecreases further the ss_(b) ⁰ mode follows closely the phase andattenuation curves of the s_(b) mode supported by the metal film slabwaveguide. In addition to exhibiting dispersion, the lower branch modeschange in character with decreasing thickness, their fields evolvingfrom being concentrated near the corners, to having Gaussian-likedistributions along the waveguide width. The E_(y) field component ofthe ss_(b) ⁰ mode develops an extremum near the center of the top andbottom interfaces, while that of the as_(b) ⁰ mode develops two extrema,one on either side of the center. Since these modes change in character,they should be identified when the film is fairly thick.

FIGS. 7(a) to 7(f) show the evolution of the ss_(b) ⁰ mode fields withfilm thickness via contour plots of Re{S_(z)}. S_(z) is computed fromthe ss_(b) ⁰ mode fields using Equation 13 and corresponds to thecomplex power density carried by the mode. The power confinement factorcf is also given in the figure for all cases, and is computed viaequation (12) with the area of the waveguide core A_(c) taken as thearea of the metal region. FIGS. 7(a) to 7(f) clearly show how the modefields evolve from being confined to the corners of thick films to beingdistributed in a Gaussian-like manner laterally along the top and bottomedges, as the field coupling between these edges increases due to areduction in film thickness. The confinement factor becomes smaller asthe film thickness decreases, ranging from 14% confinement to 1.6% asthe thickness goes from 80 nm to 20 nm. This implies that fields becomeless confined to the metal, spreading out not only along the verticaldimension but along the horizontal one as well, as is observed bycomparing FIGS. 7(a) and 7(b). This reduction in confinement to thelossy metal region explains the reduction in the attenuation constant ofthe mode with decreasing film thickness, as shown in FIG. 2(b). Anexamination of all field components related to the ss_(b) ⁰ mode revealsthat the magnitudes of the weak transverse (E_(x), H_(y)) andlongitudinal (E_(z), H_(z)) components decrease with decreasing filmthickness, implying that the mode is evolving towards a TEM modecomprised of the E_(y) and H_(x) field components. Indeed, thenormalized propagation constant of the ss_(b) ⁰ mode tendsasymptotically towards the value of the normalized propagation constantof a TEM wave propagating in the background material (ε_(r,1)=4 with nolosses in this case), further supporting this fact. This field behaviouris also consistent with that of the s_(b) mode supported by a metal filmslab waveguide.

FIG. 8 shows the profile of Re{S_(z)} of the ss_(b) ⁰ mode over thecross-section of the guide for the case t=20 nm, providing a differentperspective of the same information plotted as contours in FIG. 7(f).FIG. 8 shows that Re{S_(z)} is negative in the metal film, implying thatthe mode real power is flowing in the direction opposite to thedirection of mode propagation (or to the direction of phase velocity) inthis region. It is clear however that the overall or net mode real poweris flowing along the direction of propagation. It is possible that thenet mode real power can be made to flow in the direction opposite tothat of phase velocity (as in metal film slab waveguides [10]) forvalues of ε_(r,1) in the neighbourhood or greater than |Re{ε_(r,2)}|.

Unlike the metal film slab waveguide, a metal film of finite width cansupport a number of higher order modes. The dispersion curves of thefirst four higher order modes (each generated from one of the symmetrieslisted in Table 1 are shown in FIGS. 2(a) and 2(b), and the spatialdistribution of their main transverse electric field component is shownin FIG. 9 for a film of thickness t=100 nm. As is observed from FIGS.9(a) to 9(d), the symmetries and number of extrema in the distributionsof Re{E_(y)} are reflected in the mode nomenclature. It should be notedthat the nature of the nomenclature is such that all higher order modessa_(b) ^(m) and ss_(b) ^(m) have an odd m while all higher order modesaa_(b) ^(m) and as_(b) ^(m) have an even m. Comparing FIGS. 9(a) to 9(d)with FIGS. 3(c), 4(c), 5(c) and 6(c), respectively, (ie: comparing theE_(y) component of the ss_(b) ¹ mode shown in FIG. 9(a) with the E_(y)component of the ss_(b) ⁰ mode shown in FIG. 3(c), etc . . . ) revealsthat the fields of a higher order mode are comprised of the fields ofthe corresponding m=0 mode with additional spatial oscillations orvariations along the top and bottom edges of the structure due to thelatter's limited width. Making this comparison for all of the fieldcomponents of the higher order modes found reveals this fact to be true,except for the H_(y) field component which remains in all casesessentially identical to that of the corresponding m=0 mode; ie: theH_(y) field component never exhibits oscillations along the width of thestructure.

The evolution of the sa_(b) ¹ and aa_(b) ² modes with film thickness issimilar to the evolution of the sa_(b) and aa_(b) ⁰ modes (and the a_(b)mode supported by the metal film slab waveguide), in that their modefields become more tightly confined to the metal as the thickness of thelatter decreases, thereby causing an increase in the attenuation of themodes, as shown in FIG. 2(b). Furthermore, the sa_(b) ¹ and aa_(b) ²modes do not change in character with film thickness, their fielddistributions remaining essentially unchanged in appearance from thosecomputed at a thickness of 100 nm.

The ss_(b) ¹ and as_(b) ² modes evolve with thickness in a mannersimilar to the corresponding m=0 modes (and the s_(b) mode of the metalfilm slab waveguide) in the sense that their fields become less confinedto the metal region as the thickness of the latter decreases, therebyreducing the attenuation of the modes as shown in FIG. 2(b). As thethickness of the film decreases, the ss_(b) ¹ and as_(b) ² modes changein character in a manner similar to the corresponding m=0 modes, theirfield components evolving extra variations along the top and bottomedges.

As the thickness of the film increases, the propagation constants of thesa_(b) ¹ and ss_(b) ¹ modes converge to a single complex value as shownin FIGS. 2(a) and 2(b). This is the propagation constant of uncoupledhigher order modes supported by the top and bottom edges of the film. Asimilar observation holds for the aa_(b) ² and as_(b) ² modes. Thenature of these ‘edge modes’ is clear by considering the evolution withincreasing film thickness of the distributions shown in FIGS. 9(a) to9(d). As the thickness of the film tends to infinity, the top edgebecomes uncoupled from the bottom edge, forcing the ss_(b) ¹ mode tobecome degenerate with the sa_(b) ¹ mode since both have an E_(y) fieldcomponent that is symmetric with respect to the y axis and one extremumin its distribution along the top or bottom edge. A similar reasoningexplains why the as_(b) ² mode must become degenerate with the ss_(b) ²mode. In general, it is expected that the higher order sa_(b) ^(m) andss_(b) ^(m) mode families will form degenerate pairs for a given m, aswill the higher order as_(b) ^(m) and aa_(b) ^(m) mode families, withincreasing film thickness.

The aa_(b) ^(m) and sa_(b) ^(m) mode families do not have mode cutoffthicknesses. This is due to the fact that their confinement to the metalfilm increases with decreasing film thickness; thus the modes remainguided as t→0. The as_(b) ^(m) and ss_(b) ^(m) mode families have cutoffthicknesses for all modes except the ss_(b) ⁰ mode, which remains guidedas t→0, since it evolves into the TEM mode supported by the background.The other modes of these families, including the as_(b) ⁰ mode cannotpropagate as t→0 because their mode fields do not evolve into a TEMmode. Rather, the modes maintain extrema in their field distributionsand such variations cannot be enforced by an infinite homogeneousmedium.

In general, the purely bound modes supported by a metal film of finitewidth appear to be formed from a coupling of modes supported by eachmetal-dielectric interface defining the structure. In a metal film offinite width, straight interfaces of finite length (top, bottom, leftand right edges) and corner interfaces are present. Since a straightmetal-dielectric interface of infinite length can support a boundplasmon-polariton mode then so should an isolated corner interface and astraight interface of finite length bounded by corners (say the edgedefined by a metal of finite width having an infinite thickness). Apreliminary analysis of an isolated corner has revealed that aplasmon-polariton mode is indeed supported and that the phase andattenuation constants of this mode are greater than those of the modeguided by the corresponding infinite straight interface, as given byEquations (14) and (15). This is due to the fact that fields penetratemore deeply into the metal near the corner, to couple neighbouringperpendicular edges. All six field components are present in such amode, having their maximum value at the corner and decreasing in anexponential-like manner in all directions away from the corner. Astraight interface of finite length bounded by corners should support adiscrete spectrum of plasmon-polariton modes with the defining featurein the mode fields being the number of extrema in their spatialdistribution along the edge. A mode supported by a metal film of finitewidth: may therefore be seen as being comprised of coupled ‘cornermodes’ and ‘finite length edge modes’.

The ss_(b) ⁰ mode could be used for optical signal transmission overshort distances. Its losses decrease with decreasing film thickness in amanner similar to the s_(b) mode supported by the metal film slabwaveguide. In a symmetric waveguide structure such as the one studiedhere, the ss_(b) ⁰ mode does not have a cut-off thickness so lossescould be made small enough to render it long-ranging, though a trade-offagainst confinement is necessary. In addition, when the metal is thin,the E_(y) field component of the mode has a maximum near the center ofthe metal-dielectric interfaces, with a symmetric profile similar tothat shown in FIG. 8. This suggests that the mode should be excitableusing a simple end-fire technique similar to the one employed to excitesurface plasmon-polariton modes [19,6]; this technique is based onmaximizing the overlap between the incident field and that of the modeto be excited.

In reference [22], the present inventor et al. disclosed thatplasmon-polariton waves supported by thin metal films of finite widthhave recently been observed experimentally at optical communicationswavelengths using this method of excitation.

IV. Mode Dispersion With Film Width: Symmetric Structures

Since the modes supported by a metal film waveguide exhibit dispersionwith film thickness, it is expected that they also exhibit dispersionwith film width.

A. Modes Supported by a Metal Film of Width w=0.51 μm

The analysis of a metal film waveguide of width w=0.5 μm will now bediscussed, using the material parameters and free-space wavelength thatwere used in the previous section. A film width of 0.5 μm was selectedin order to determine the impact of a narrowing film on the modessupported and to demonstrate that the structure can still function as awaveguide though the free-space optical wavelength is greater than boththe width and thickness of the film.

As in the previous section, the first eight modes supported by thestructure (two for each symmetry listed in Table 1) were sought, but inthis case only six modes were found. The dispersion curves withthickness of the modes found are plotted in FIGS. 10(a) and 10(b). Theobservations made in the previous section regarding the generalbehaviour of the modes hold for other film widths, including this one.

The aa_(b) ² and as_(b) ² modes, which were the highest order modesfound for a film of width w=1 μm, were not found in this case suggestingthat the higher order modes (m>0) in general have a cut-off width.Comparing FIG. 10(a) with FIG. 2(a), it is apparent that decreasing thefilm width causes a decrease in the phase constant of the ss_(b) ¹ andsa_(b) ¹ modes, further supporting the existence of a cut-off width forthese modes.

Comparing FIGS. 10(a) and 10(b) with FIGS. 2(a) and 2(b), it is notedthat the modes which do exhibit cutoff thicknesses (the ss_(b) ^(m)modes with m>0 and the as_(b) ^(m) modes with m≧0), exhibit them at alarger thickness for a narrower film width. This makes it possible todesign a waveguide supporting only one long-ranging mode (the ss_(b) ⁰mode) by carefully selecting the film width and thickness.

B. Dispersion of the ss_(b) ⁰ Mode With Film Width

The dispersion with thickness of the ss_(b) ⁰ mode is shown in FIGS.11(a) and 11(b) for numerous film widths in the range 0.25≦w≦1 μm,illustrating the amount of dispersion in the mode properties that can beexpected due to a varying film width. In all cases, the ss_(b) ⁰ modeevolves with decreasing film thickness into the TEM wave supported bythe background, but this evolution occurs more rapidly for a narrowerwidth. For a film of thickness t=20 nm, for example, from FIG. 11(a),the normalized phase constant of the mode supported by a film of widthw=1 μm is about 2.05, while that of the mode supported by a film ofwidth w=0.25 μm is already about 2. This fact is also supported by theresults plotted in FIG. 11(b) since the attenuation constant of the modeat a thickness of t=20 nm is closer to zero (the attenuation constant ofthe background) for narrow film widths compared to wider ones. Indeed,at a thickness of 10 nm, the attenuation of the mode for a width ofw=0.25 μm is more than an order of magnitude less than its attenuationat a width of w=1 μm (and more than an order of magnitude less than thatof the s_(b) mode supported by a metal film slab waveguide), indicatingthat this mode can be made even more long-ranging by reducing both thefilm thickness and its width.

The dispersion of the mode with increasing film thickness also changesas a function of film width, as seen from FIG. 11(a). This is due to thefact that the amount of coupling between corners along the top andbottom edges increases as the film narrows, implying that the mode doesnot evolve with increasing thickness towards a plasmon-polariton modesupported by an isolated corner, but rather towards a plasmon-polaritonmode supported by the pair of corners coupled via these edges.

FIGS. 12(a) to 12(d) show contour plots of Re{S_(z)} related to thess_(b) ⁰ mode supported by films of thickness t=20 nm and variouswidths. The power confinement factor is also given for all cases, withthe area of the waveguide core A_(c) taken as the area of the metalregion. FIGS. 12(a) to 12(d) clearly illustrate how the fields becomeless confined to the lossy metal as its width decreases, explaining thereduction in attenuation shown in FIG. 11(b) at this thickness. Inaddition, the confinement factor ranges from 1.64% to 0.707% for thewidths considered, further corroborating this fact. The fields are alsoseen to spread out farther, not only along the horizontal dimension butalong the vertical one as well, as the film narrows. This indicates thatthe mode supported by a narrow film is farther along in its evolutioninto the TEM mode supported by the background, compared to a wider filmof the same thickness. It is also clear from FIGS. 12(a) to 12(d) thatthe trade-off between mode confinement and attenuation must be made byconsidering not only the film thickness but its width as well.

V. Effects Caused by Varying the Background Permittivity: SymmetricStructures

In this section, the changes in the propagation characteristics of thess_(b) ⁰ mode due to variations in the background permittivity of thewaveguide. Only the ss_(b) ⁰ mode is considered since the main effectsare in general applicable to all modes. In order to isolate the effectscaused by varying the background permittivity, the width of the metalfilm was fixed to w=0.5 μm and its permittivity as well as the opticalfree-space wavelength of analysis were set to the values used in theprevious sections. The relative permittivity of the background ε_(r,1)was taken as the variable parameter.

The dispersion with thickness of the ss_(b) ⁰ mode is shown in FIG. 13for some background permittivities in the range 1≦ε_(r,1)≦4. FIGS. 14(a)to 14(d) compare contour plots of Re{S_(z)} related to this mode for afilm of thickness t=20 nm and for the same set of backgroundpermittivities used to generate the curves plotted in FIG. 13. FromFIGS. 14(a) to 14(d); it is observed that reducing the value of thebackground permittivity causes a reduction in field confinement to themetal. This reduction in field confinement within the lossy metal inturn causes a reduction in the attenuation of the mode that can be quitesignificant, FIG. 13 showing a reduction of almost four orders ofmagnitude at a film thickness of t=20 nm, as the background relativepermittivity ranges from ε_(r,1)=4 to 1. It is also noted that the modeexhibits less dispersion with thickness as the background relativepermittivity is reduced, since the normalized phase constant curvesshown in FIG. 13 flatten out with a reduction in the value of thisparameter.

From FIGS. 14(a) to 14(d), it is seen that the mode power is confined towithin approximately one free-space wavelength in all directions awayfrom the film in all cases except that shown in FIG. 14(d), where fieldsare significant up to about two free-space wavelengths. In FIG. 14(c),the background permittivity is roughly that of glass and from FIG. 13the corresponding normalized attenuation constant of the mode is aboutα/β₀=6.0×10⁻⁵. The associated mode power attenuation in dB/mm, computedusing the following formula: $\begin{matrix}{{Att} = {\alpha \times \frac{20}{1000}{\log_{10}(e)}}} & (16)\end{matrix}$

is about 5 dB/mm. This value of attenuation is low enough and fieldconfinement is high enough as shown in FIG. 14(c), to render thisparticular structure practical at this free-space wavelength forapplications requiring short propagation lengths.

The changes in mode properties caused by varying the backgroundpermittivity as discussed above are consistent with the changes observedfor the modes supported by a metal film slab waveguide and theobservations are in general applicable to the other modes supported by ametal film of finite width. In the case of the higher order modes (m>0)and those exhibiting a cutoff thickness (the as_(b) ^(m) modes for all mand the ss_(b) ^(m) modes for m>0) additional changes in the modeproperties occur. In particular, as the background permittivity isreduced, the cut-off widths of the higher order modes increase as do allrelevant cut-off thicknesses.

VI. Frequency Dependency of the ss_(b) ⁰ Mode Solutions: SymmetricStructures

In order to isolate the frequency dependency of the ss_(b) ⁰ modesolutions, the geometry of the metal film was held constant and thebackground relative permittivity was set to ε_(r,1)=4. The relativepermittivity of the metal film ε_(r,2) was assumed to vary with thefrequency of excitation according to Equation (1). In order to remainconsistent with [6], the values ω_(p)=1.29×10¹⁶ rad/s and1/ν=τ=1.25×10⁻¹⁴ s were adopted, though the latter do not generateexactly ε_(r,2)=−19−j0.53 at λ₀=0.633 μm, which is the value used in theprevious sections. This is due to the fact that values of ω_(p) and τare often deduced by fitting Equation (1) to measurements. The valuesused, however, are in good agreement with recent measurements made forsilver [3] and are expected to generate frequency dependent results thatare realistic and experimentally verifiable.

The dispersion characteristics of the ss_(b) ⁰ mode supported by filmsof width w=0.5 μm and w=1 μm, and thicknesses in the range 10≦t≦50 nmare shown in FIGS. 15(a) and 15(b) for frequencies covering thefree-space wavelength range 0.5≦λ₀23−2 μm. Curves for the s_(b) modesupported by metal film slab waveguides (w=∞) of the same thicknessesare also shown for comparison.

The results given in FIG. 15(a) show that, in all cases, the normalizedphase constant of the modes tends asymptotically towards that of the TEMwave supported by the background as the wavelength increases, and thatthe convergence to this value is steeper as the width of the filmdecreases (for a given thickness). The curves remain essentiallyunchanged in character as the thickness changes, but they shift upwardstoward the top left of the graph with increasing thickness, as shown.Convergence to the asymptote value with increasing wavelength suggeststhat the ss_(b) ⁰ mode evolves into the TEM mode supported by thebackground. It is noteworthy that the ss_(b) ⁰ mode can exhibit verylittle dispersion over a wide bandwidth, depending on the thickness andwidth of the film, though flat dispersion is also associated with lowfield confinement to the metal film.

The results plotted in FIG. 15(b) show in all cases a decreasingattenuation with increasing wavelength and the curves show a sharperdrop for a narrow film (w=0.5 μm) compared to a wide one (w=∞). Theattenuation curves look essentially the same for all of the filmthicknesses considered, though the range of attenuation values shiftsdownwards on the graph with decreasing film thickness.

FIGS. 16(a) to 16(f) give contour plots of Re{S_(z)} related to thess_(b) ⁰ mode for films of thickness t=20 nm and widths w=0.5 μm and w=1μm, for three free-space wavelengths of operation: λ₀=0.6, 0.8 and 1.21μm. Comparing the contours shown in FIGS. 16(a) to 16(f), explains inpart the frequency dependent behaviour plotted in FIGS. 15(a) and 15(b).FIGS. 16(a) to 16(f) show that the mode power contours spread outfarther from the film as the wavelength increases, which means that themode confinement to the metal region decreases, explaining in part thedecrease in losses and the evolution of the mode towards the TEM mode ofthe background, as shown in FIGS. 15(a) and 15(b). This behaviour ismore pronounced for the waveguide of width w=0.5 μm compared to thewider one of width w=1.0 μm.

There are two mechanisms causing changes in the ss_(b) ⁰ mode as thefrequency of operation varies. The first is geometrical dispersion,which changes the optical or apparent size of the film, and the secondis material dispersion, which is modelled for the metal region usingEquation (1). If no material dispersion is present, then the geometricaldispersion renders the film optically smaller as the free-spacewavelength is increased (an effect similar to reducing t and w) so, inthe case of the ss_(b) ⁰ mode, confinement to the film is reduced andthe mode spreads out in all directions away from the latter. Now basedon Equation (1), it is clear that the magnitude of the real part of thefilm's permittivity |Re{ε_(r,2)}| varies approximately in a 1/ω² or λ₀ ²fashion while the magnitude of its imaginary part |Im{ε_(r,2)}| variesapproximately in a 1/ω³ or λ₀ ³ fashion. However, an increase in|Re{ε_(r,2)}| reduces the penetration depth of the mode fields into themetal region and, combined with the geometrical dispersion, causes a netdecrease in mode attenuation with increasing wavelength, even though thelosses in the film increase in a λ₀ ³ fashion.

FIG. 15(b) shows that mode power attenuation values in the range 10 to0.1 dB/cm are possible near communications wavelengths (λ₀ ^(˜)1.5 μm)using structures of reasonable dimensions: w^(˜)1.0 μm and t^(˜)15 nm.Such values of attenuation are low enough to consider the ss_(b) ⁰ modeas being long-ranging, suggesting that these waveguides are practicalfor applications requiring propagation over short distances. As shown inthe previous section, even lower attenuation values are possible if thebackground permittivity is lowered. From FIGS. 16(e) and 16(f), (caseλ₀1.2 μm, which is near communications wavelengths), it is apparent thatthe mode power confinement is within one free-space wavelength of thefilm, which should be tight enough to keep the mode bound to thestructure if a reasonable quality metal film of the right geometry canbe constructed.

VII. Mode Characteristics and Evolution With Film Thickness: SmallAsymmetry

A. Mode Solutions for a Metal Film Slab Waveguide

Effects on waveguiding characteristics of using an asymmetric waveguidestructure will now be discussed, beginning with the reproduction ofresults for an infinitely wide asymmetric metal film waveguide (similarto that shown in FIG. 17(a) but with w=∞), taken from the standard workon such structures [6]. In order to remain consistent with theirresults, the optical free-space wavelength of excitation is set toλ₀=0.633 μm and the value they used for the relative permittivity of thesilver film at this wavelength is used here: ε_(r,2)=19−j0.53. Therelative permittivities of the bottom and top dielectric regions are setto ε_(r,1)=4 (n₁=2) and ε_(r,3)=3.61 (n₃=1.9); these values create astructure having a small asymmetry with respect to the horizontaldimension.

The dispersion curves of the s_(b) and a_(b) modes supported by theinfinitely wide structure were computed using the MoL and the resultsare shown in FIGS. 18(a) and 18(b). From these figures, it is seen thatthe propagation constant of the a_(b) mode tends towards that of theplasmon-polariton mode supported by the bottom interface, given byEquations (14) and (15), as the thickness of the film increases. It isalso noted that this mode does not exhibit a cutoff thickness, while itis clear that the s_(b) mode has one near t=18 nm. The propagationconstant of the s_(b) mode is seen to tend towards the value of aplasmon-polariton mode supported by the top interface as the thicknessincreases. These results are in perfect agreement with those reported in[6].

B. Modes Supported by a Metal Film of Width w=1 μm

The study proceeds with the analysis of the structure shown in FIG.17(a) for the case w=1 μm. The material parameters and free-spacewavelength that were used in the previous case w=∞ were also used here.The dispersion curves for the first seven modes were computed using theMoL and the results are shown in FIGS. 18(a) and 18(b).

In this asymmetric structure, true field symmetry exists only withrespect to the y axis. With respect to the horizontal dimension, themodes have a symmetric-like or asymmetric-like field distribution withfield localization along either the bottom or top metal-dielectricinterface. The modes that have a symmetric-like distribution withrespect to the horizontal dimension are localized along themetal-dielectric interface with the lowest dielectric constant, whilemodes that have an asymmetric-like distribution with respect to thisaxis are localized along the metal-dielectric interface with the highestdielectric constant. This behaviour is consistent with that observed forasymmetric metal slab waveguides.

The mode nomenclature adopted for symmetric structures can be usedwithout ambiguity to describe the modes supported by asymmetricstructures as long as the modes are identified when the metal film isfairly thick, before significant coupling begins to occur through themetal film, and while the origin of the mode can be identifiedunambiguously. As the metal film thickness decreases, the modes (andtheir fields) can evolve and change considerably more in an asymmetricstructure compared to a symmetric one. The number of extrema in the maintransverse electric field component of the mode is counted along thelateral dimension at the interface where the fields are localized. Thisnumber is then used in the mode nomenclature.

It was observed in Section III that the modes supported by symmetricstructures are in fact supermodes created from a coupling of “edge” and“corner” modes supported by each metal-dielectric interface defining thestructure. As the thickness and width of the metal decrease, thecoupling between these interface modes intensifies leading to dispersionand possibly evolution of the supermode. In asymmetric structures, thebound modes are also supermodes created in a similar manner, except thatdissimilar interface modes may couple to each other to create thesupermode. For instance, a mode having one field extremum along the topinterface (along the top edge bounded by the corners) may couple with amode having three extrema along the bottom interface. The main selectioncriterion determining which interface modes will couple to create thesupermode is similarity in the value of their propagation constants. Forall modes supported by an asymmetric structure, an apparent symmetry orasymmetry with respect to the horizontal dimension can still be observedin the corner modes.

The sa_(b) ⁰, aa_(b) ⁰, ss_(b) ⁰ and as_(b) ⁰ modes are the fundamentalmodes supported by the structure. The sa_(b) ⁰ and aa_(b) ⁰ modes arecomprised of coupled corner modes, resembling the corresponding modes ina symmetric structure, except that the fields are localized near thesubstrate. These two modes do not change in character as the thicknessof the film decreases. A narrowing of the metal film would eventuallybreak the degeneracy observed in FIGS. 18(a) and 18(b).

For a sufficiently large thickness (about 100 nm for the presentstructure), the ss_(b) ⁰ and as_(b) ⁰ modes are comprised of coupledcorner modes much like the corresponding modes in a symmetric structureexcept that the fields are localized near the superstrate. As thethickness of the metal film decreases, both of these modes begin toevolve, changing completely in character for very thin films. FIGS.19(a) to 19(d) show the evolution of the E_(y) field component relatedto the ss_(b) ⁰ mode as the thickness of the film ranges from 100 nm(FIG. 19(a)) to 40 nm (FIG. 19(d)). It is clearly seen that the modeevolves from a symmetric-like mode having fields localized near thesuperstrate to an asymmetric-like mode having fields localized along thesubstrate-metal interface. A similar evolution is observed for theas_(b) ⁰ mode. This change in character is also apparent in theirdispersion curves: they follow the general behaviour of a symmetric-likemode for large thicknesses but then slowly change to follow thebehaviour of an asymmetric-like mode as the thickness decreases. Sincethe substrate dielectric constant is larger than the superstratedielectric constant, the mode is “pulled” from a symmetric-like mode toan asymmetric-like mode (having field localization at thesubstrate-metal interface) as the metal film becomes thinner.

FIGS. 20(a) to 20(d) show the E_(y) field component related to thess_(b) ¹ and sa_(b) ¹ modes for two film thicknesses. From these Figuresit is noted that the top and bottom edge modes comprising a supermodeare different from each other. In FIG. 20(a), for instance, it is seenthat the bottom edge mode has three extrema and is of higher order thanthe top edge mode which has one extremum. A similar observation holdsfor FIG. 20(c), where it can be seen that the bottom edge mode has oneextremum while the top one has none. In this structure, the substratehas a higher dielectric constant than the superstrate so the phaseconstant of a particular substrate-metal interface mode will be higherthan the phase constant of the same mode at the metal-superstrateinterface. Since a supermode is created from a coupling of edge modeshaving similar propagation constants, it should be expected that, in anasymmetric structure, different edge modes may couple to create asupermode. In general, higher-order modes have smaller values of phaseconstant compared to lower-order modes, so in structures having ε₃<ε₁,all supermodes are comprised of a bottom edge mode of the same order orhigher than the top edge mode, as shown in FIGS. 20(a) to 20(d). Ifε₃>ε₁, then the opposite statement is true.

A careful inspection of the fields associated with the ss_(b) ¹, sa_(b)¹ and aa_(b) ² modes reveals that, as the thickness of the filmdecreases, the mode fields may evolve in a smooth manner similar to thatshown in FIGS. 19(a) to 19(d), but, in addition, a change or “switch” ofthe constituent edge modes may also occur. For instance, from FIG.20(c), the sa_(b) ¹ mode is seen to comprise a substrate-metal interfacemode having one extremum for a film thickness of 100 nm, while for athickness of 60 nm the substrate-metal interface mode has three extrema,as shown in FIG. 20(d). Since higher-order modes have in general lowerphase constants than lower-order modes, this change in edge modes causesa reduction in the phase constant of the sa_(b) ¹ mode in theneighbourhood of 60 nm, as shown in FIG. 18(a). Another change occursnear 40 nm as the corner modes switch from being symmetric-like (as inFIGS. 20(c) and 20(d)) to being asymmetric-like with respect to thehorizontal dimension. This change is again reflected in the dispersioncurve of the sa_(b) ¹ mode as its phase constant is seen to increasewith a further decrease in thickness. In general, the changes in theedge and corner modes are consistent with the directions taken by thedispersion curves as the film thickness decreases, thus explaining theoscillations in the curves seen in FIGS. 18(a) and 18(b).

The only potentially long-ranging mode supported by this structure atthe wavelength of analysis is the ss_(b) ¹ mode. As shown in FIGS. 18(a)and 18(b), the mode has a cutoff thickness near t=22 nm and although theattenuation drops quickly near this thickness, it should be rememberedthat the field confinement does so as well. Furthermore, the spatialdistribution of the main transverse field component related to this modeevolves with decreasing thickness in the manner shown in FIGS. 20(a) and20(b), such that near cutoff the spatial distribution has strong extremaalong the top and bottom edges. These extrema render the mode lessexcitable using an end-fire technique, so coupling losses would behigher compared to the fundamental symmetric mode in symmetricwaveguides. Also, the fact that the mode would be operated near itscutoff thickness implies that very tight tolerances are required in thefabrication of structures. Nevertheless, it should be possible toobserve propagation of this mode in a suitable structure using anend-fire experiment.

VIII. Mode Characteristics and Evolution With Film Thickness: LargeAsymmetry

A. Mode Solutions for a Metal Film Slab Waveguide

The study proceeds with the analysis of structures having a largedifference in the dielectric constants of the substrate and superstrate.With respect to FIG. 17(a), the relative permittivities of the substrateand superstrate are set to ε_(r,1)=4 (n₁=2) and ε_(r,3)=2.25 (n₃=1.5),respectively, the width of the metal film is set to w=∞, and thedielectric constant of the metal region and the wavelength of analysisare set to the same values as in Section III. The dispersion curves ofthe s_(b) and a_(b) modes supported by this structure can be seen inFIGS. 21(a) and 21(b). Comparing with FIGS. 18(a) and 18(b), it isobserved that the s_(b) mode has a larger cutoff thickness in astructure having a large asymmetry than in a structure having similarsubstrate and superstrate dielectric constants. The results shown werecomputed using the MoL and are in perfect agreement with those reportedin [6].

B. Modes Supported by a Metal Film of Width w=1 μm

The structure shown in FIG. 17(a) was analyzed using the MoL for w=1 μmand for the same material parameters and free-space wavelength as thosegiven above for w=∞. The dispersion curves of the first six modessupported by the structure are shown in FIGS. 21(a) and 21(b).

An inspection of the mode fields related to the sa_(b) ⁰ and aa_(b) ⁰modes reveals that these modes are again comprised of coupled cornermodes with fields localized at the substrate-metal interface. The modesdo not change in character as the thickness of the film decreases and anarrowing of the metal film would eventually break the degeneracyobserved in FIGS. 21(a) and 21(b).

The spatial distribution of the E_(y) field component related to the,ss_(b) ⁰, as_(b) ⁰, sa_(b) ¹ and aa_(b) ² modes is given in FIGS. 22(a)to 22(d). It is noted from this figure that in all cases themetal-superstrate interface modes are similar: they have fields with noextrema along the interface but rather that are localized near thecorners and have either a symmetric or asymmetric distribution withrespect to the y axis. These corner modes are in fact the lowest ordermodes supported by the metal-superstrate interface; they have thelargest value of phase constant and thus are most likely to couple withedge modes supported by the substrate-metal interface to form asupermode. From FIGS. 22(a) and 22(b) it is observed that thesubstrate-metal interface modes comprising the ss_(b) ⁰ and as_(b) ⁰modes are of very high order. This is expected since the substratedielectric constant is significantly higher than the superstratedielectric constant and higher order modes have lower values of phaseconstant.

The ss_(b) ⁰ and as_(b) ⁰ modes shown in FIGS. 22(a) and 22(b) indeedhave fields that are localized along the metal-superstrate interface,while the sa_(b) ¹ and aa_(b) ² modes shown in FIGS. 22(c) and 22(d)have fields that are localized along the substrate-metal interface.

One effect, caused by increasing the difference between the substrateand superstrate dielectric constants, is that the difference between theorders of the top and bottom edge modes comprising a supermode canincrease. This effect can be observed by comparing FIG. 19(a) with FIG.22(a). In the former, there is no difference between the orders of thetop and bottom edge modes, while in the latter the difference in theorders is 5. Another effect is that the degree of field localizationincreases near the interface between the metal and the dielectric ofhigher permittivity, for all modes that are asymmetric-like with respectto the horizontal dimension. This effect can be seen by comparing thefields related to the sa_(b) ¹ mode shown in FIGS. 22(c) and 20(c). Acomparison of the fields related to the sa_(b) ⁰ and aa_(b) ⁰ modesreveals that this effect is present in these modes as well.

From the dispersion curves shown in FIG. 21(a), it is apparent that thenormalized phase constant of all modes converge with increasing filmthickness to normalized phase constants in the neighbourhood of thosesupported by plasmon-polariton waves localized along the associatedisolated edge. The normalized phase constants of modes having fieldslocalized at the substrate-metal interface, converge with increasingfilm thickness to normalized phase constants in the neighbourhood ofthat related to the a_(b) mode, while the normalized phase constants ofmodes having fields localized along the metal-superstrate interfaceconverge to values near that of the s_(b) mode. This behaviour ispresent though less apparent, in structures where the asymmetry issmaller, such as the one analyzed in Section VII.

Comparing FIGS. 18(a) and 18(b) with FIGS. 21(a) and 21(b), it is notedthat the dispersion curves of the modes are much smoother when thedifference in the substrate and superstrate dielectric constants islarge. This is due to the fact that the edge modes comprising thesupermodes are less likely to change or switch as they do in a structurehaving similar substrate and superstrate dielectric constants. Thusmodes that start out being symmetric-like with respect to the horizontaldimension remain so as the thickness of the film decreases. The cutoffthickness of the symmetric-like modes also increases as the differencebetween the substrate and superstrate dielectric constants increases.

It is apparent that introducing a large asymmetry can hamper the abilityof the structure to support useful long-ranging modes. Any mode that islong-ranging would likely have fields with numerous extrema along thewidth of the interface between the metal film and the dielectric ofhigher permittivity, as shown in FIGS. 22(a) and 22(b).

IX. Mode Dispersion With Film Width: Small Asymmetry

An asymmetric structure comprising the same dielectrics as thestructures studied in Section VII, but having a metal film of widthw=0.5 μm, was analyzed at the same free-space wavelength in order todetermine the impact of a narrowing film width on the modes supported.The structure was analyzed using the MoL and FIGS. 23(a) and 23(b) givethe dispersion curves obtained for the first few modes supported.

Comparing FIGS. 23(a) and 23(b) with FIGS. 18(a) and 18(b) reveals thatreducing the width of the film does not cause major changes in thebehaviour of the fundamental modes, but does have a major impact on thehigher order modes. It is noted that reducing the film width increasesthe cutoff thickness of the ss_(b) ¹ mode. This higher order mode issymmetric-like with respect to the horizontal dimension, and the cutoffthickness of the symmetric-like modes in general increases as the widthof the film decreases due to a reduction in field confinement to themetal film.

The aa_(b) ² mode was sought but not found for this film width.

It is also noted by comparing FIGS. 23(a) and 23(b) with FIGS. 18(a) and18(b) that the sa_(b) ¹ mode evolves quite differently depending on thewidth of the film. For a film width of w=1 μm, the mode follows thegeneral behaviour of an asymmetric-like mode whereas, for a film widthof w=0.5 μm, the mode evolves as a symmetric-like mode, and has a cutoffthickness near t=27 nm. When the film is wide, it becomes possible fornumerous higher order edge modes (having similar values of phaseconstant) to be supported by the substrate-metal or metal-superstrateinterfaces, so edge modes comprising a supermode are likely to change orswitch as the thickness of the film is reduced, as shown in FIGS. 20(c)and 20(d). For a narrow metal film, some of the higher order edge modesmay be cutoff, thus rendering changes in edge modes impossible. In sucha case, the supermode-may be forced to evolve in a smooth manner withdecreasing film thickness. A close inspection of the mode fields relatedto the sa_(b) ¹ mode for a film width of w=0.5 μm reveals that there areno changes to the edge modes as the thickness decreases; rather the modeevolves smoothly from its field distribution at a large thickness(similar to that shown in FIG. 20(c)) to having a symmetric-likedistribution with only one extremum along the top and bottom edges ofthe film. A change in behaviour due to a change in the width of themetal film was observed only for the sa_(b) ¹ mode in this study, butsuch changes are in general not limited to this mode.

The sa_(b) ¹ and ss_(b) ¹ modes could be made to propagate over usefuldistances in this structure, if they are excited near their cutoffthicknesses. However, the difficulties outlined in Section VII Bregarding the excitation of modes near cutoff also hold here.

X. Evolution of the ss_(b) ⁰ and sa_(b) ¹ Modes With Structure Asymmetry

The ss_(b) ⁰ and sa_(b) ¹ modes are of practical interest. The ss_(b) ⁰mode is the main long-ranging mode supported by symmetric finite-widthmetal film structures, and, as demonstrated in the previous section, thesa_(b) ¹ mode can be the main long-ranging mode supported by asymmetricfinite-width structures. In metal films of the right thickness, they arealso the modes that are the most suitable to excitation in an end-firearrangement.

Structures comprising a substrate dielectric having n₁=2, of a metalfilm of width w=0.5 μm, and of various superstrate dielectrics havingn₃=2, 1.99, 1.95 and 1.9 were analyzed at the same free-space wavelengthas in Section VII. The equivalent permittivity of the metal film wasalso set to the same value as in Section VII. These analyses wereperformed in order to investigate the effects on the propagationcharacteristics of the ss_(b) ⁰ and sa_(b) ¹ modes caused by a slightdecrease in the superstrate permittivity relative to the substratepermittivity. FIGS. 24(a) and 24(b) show the dispersion curves with filmthickness, obtained for these modes in the four structures of interest.

As seen in FIG. 24(a) and its inset, the dispersion curves of the modesintersect at a certain film thickness only for the symmetric case(n₃=n₁). As soon as some degree of asymmetry exists, the curves nolonger intersect, though they may come quite close to each other if theasymmetry is small, as seen in the case of n₃=1.99. As the degree ofasymmetry increases, the separation between the curves increases.

The evolution with film thickness of the sa_(b) ¹ mode is shown in FIGS.25(a) to 25(d) for the case n₃=1.99 and for thicknesses about t=59 nm(near the maximum in its phase dispersion curve). The evolution of thismode for the cases n₃=1.95 and 1.9 is similar to that shown. Theevolution with film thickness of the ss_(b) ⁰ mode is similar in, thesestructures to the evolution shown in FIGS. 19(a) to 19(d) for the casew=1 μm and n₃=1.9. Comparing FIGS. 25(a) to 25(d) and FIGS. 19(a) to19(d), reveals that the modes “swap” character near t=59 nm. For filmthicknesses sufficiently above this value, the modes exhibit theirdefining character as shown in FIGS. 19(a) and 25(a), but for filmthicknesses below it, each mode exhibits the other's character, as shownin FIGS. 19(d) and 25(d). This character swap is present for the threecases of asymmetry considered here (n₃=1.99, 1.95 and 1.9) and explainsthe behaviour of the dispersion curves shown in FIGS. 24(a) and 24(b).

From FIGS. 24(a) and 24(b), it is noted that a cutoff thickness existsfor the long-ranging mode as soon as an asymmetry is present in thestructure. It is also observed that the cutoff thickness increases withincreasing asymmetry. In the case of n₃=1.99, the cutoff thickness ofthe mode is near t=12 nm, while for n₃=1.9 the cutoff thickness is neart=27 nm. As the width of the metal film w increases, the cutoffthickness of the sa_(b) ¹ mode decreases as long as the mode remainslong-ranging (recall that the character of this mode may also changewith film width such that its behaviour is similar to the a_(b) mode inthe corresponding slab structure, as shown in FIGS. 18(a) and 18(b)).Also, it is clear from FIGS. 23(a) and 23(b) that the cutoff thicknessof the sa_(b) ¹ mode is greater than the cutoff thickness of the s_(b)mode supported by the corresponding slab structure. These results implythat the long-ranging mode supported by a thin narrow metal film is moresensitive to differences in the superstrate and substrate permittivitiesthan the s_(b) mode supported by the corresponding slab structure. Thisis reasonable in light of the fact that, in finite-width structures, themode fields tunnel through the metal as in slab structures, but, inaddition, the fields also wrap around the metal film.

FIG. 24(b) shows that near cutoff, the attenuation of the sa_(b) ¹ modesupported by an asymmetric structure drops much more rapidly than theattenuation of the ss_(b) ⁰ mode supported by a symmetric structure.Thus, a means for range extension, similar to that observed inasymmetric slab structures [7], exists for metal films of finite width,though the difficulties related to the excitation of a mode near itscutoff thickness, as described in Section VII B, also apply here.

FIGS. 26(a) to 26(d) show contour plots of {S_(z)} associated with thelong-ranging modes for the four cases of superstrate permittivityconsidered. S_(z) is the z-directed component of the Poynting vector andits spatial distribution is computed from the spatial distribution ofthe mode fields using:

S _(z)=(E _(x) H _(y) ^(*) −E _(y) H _(x) ^(*))/2  (6)

where H*_(x,y) denotes the complex conjugate of H_(x,y). FIG. 26(a)shows the contour plot associated with the ss_(b) ⁰ mode supported by asymmetric structure (n₃=n₁=2) of thickness t=20 nm. FIGS. 26(b), (c) and(d) show contours associated with the sa_(b) ¹ mode for the three casesof structure asymmetry considered. The contour plots shown in FIGS.26(b), (c) and (d) are computed for film thicknesses slightly abovecutoff, representative of the thicknesses that would be used to observethese long-ranging modes experimentally. From those figures, it is notedthat the contour plots become increasingly distorted and the fieldsincreasingly localized at the metal-superstrate interface as the degreeof asymmetry in the structure increases. It is also apparent bycomparing FIGS. 26(a) and 26(d), that in an end-fire experiment, lesspower should be coupled into the sa_(b) ¹ mode supported by theasymmetric structure with n₃=1.9, compared to the ss_(b) ⁰ modesupported by the symmetric structure. End-fire coupling losses seem toincrease with increasing structure asymmetry.

The high sensitivity of the long-ranging mode supported by thin metalfilms of finite width, to structure asymmetry, is potentially useful. Asmall induced asymmetry (created via an electro-optic effect present inthe dielectrics say) can evidently effect a large change in thepropagation characteristics of the long-ranging mode. From FIGS. 24(a)and 24(b), it is apparent that a difference between the substrate andsuperstrate refractive indices as small as n₁-n₃=Δn=0.01 is sufficientto create an asymmetric structure where the long-ranging mode has acutoff thickness of about t=12 nm. From FIG. 24(a), a slightly largerdifference of Δn=0.05 changes the normalized phase constant of thelong-ranging mode by Δ(β/β₀)≈0.025 for a metal film thickness of t=20nm. Both of these effects are potentially useful.

Asymmetric structures having superstrate dielectric constants that areslightly greater than that of the substrate were also analyzed. Thesubstrate dielectric constant was set to n₁₌2 and superstratedielectrics having n₃=2.01, 2.05 and 2.1 were considered for the samemetal, film width and operating wavelength. The results are similar tothose presented in FIGS. 24 through 26 and the cut-off thicknesses arenear those shown in FIG. 24(b). Though the results are not identical,there is no major difference between the behaviour of the ss_(b) ⁰ andsa_(b) ¹ modes whether ε₁>ε₂ or ε₁<ε₃ as long as the permittivities aresimilar.

XI. Conclusion

The purely bound optical modes supported by thin lossy metal films offinite width, embedded in an “infinite” homogeneous dielectric have beencharacterized and described. The modes supported by these symmetricstructures are divided into four families depending on the symmetry oftheir mode fields and none of the modes are TM in nature (as they are inthe metal film slab waveguide). In addition to the four fundamentalmodes that exist, numerous higher order modes are supported as well. Aproposed mode nomenclature suitable for identifying them has beendiscussed. The dispersion of the modes with film thickness has beenassessed and the behaviour in general terms found to be consistent withthat of the purely bound modes supported by the metal film slabwaveguide. In addition, it has been found that one of the fundamentalmodes and some higher order modes have cut-off thicknesses. Modedispersion with film width has also been investigated and it has beendetermined that the higher order modes have a cut-off width, below whichthey are no longer propagated. The effect of varying the backgroundpermittivity on the modes has been investigated as well, and the generalbehaviour found to be consistent with that of the modes supported by ametal film slab waveguide. In addition it was determined that thecut-off width of the higher order modes decreases with decreasingbackground permittivity and that all cut-off thicknesses are increased.

One of the fundamental modes supported by the symmetric structures, thess_(b) ⁰ mode, exhibits very interesting characteristics and ispotentially quite useful. This mode evolves with decreasing filmthickness towards the TEM wave supported by the background, (anevolution similar to that exhibited by the s_(b) mode in metal film slabwaveguides), its losses and phase constant tending asymptoticallytowards those of the TEM wave. In addition, it has been found thatdecreasing the film width can reduce the losses well below those of thes_(b) mode supported by the corresponding metal film slab waveguide.Reducing the background permittivity further reduces the losses.However, a reduction in losses is always accompanied by a reduction infield confinement to the waveguide core, which means that both of theseparameters must be traded-off one against the other. Furthermore,carefully selecting the film's thickness and width can make the ss_(b) ⁰mode the only long-ranging mode supported. It has also been demonstratedthat mode power attenuation values in the range of 10 to 0.1 db/cm areachievable at optical communications wavelengths, with even lower valuespossible. Finally, evolved into its most useful form, the ss_(b) ⁰ modehas a field distribution that renders it excitable using end-firetechniques.

The existence of the ss_(b) ⁰ mode in a symmetric structure, as well asits interesting characteristics, makes the finite-width metal filmwaveguide attractive for applications requiring short propagationdistances. The waveguide offers two-dimensional field confinement in thetransverse plane, rendering it useful as the basis of an integratedoptics technology. Interconnects, power splitters, power couplers andinterferometers could be built using the guides. Finally, the structuresare quite simple and so should be inexpensive to fabricate.

The long-ranging modes supported by asymmetric structures of finitewidth have a rapidly diminishing attenuation near their cutoff thickness(like asymmetric slab structures). The rate of decrease of theattenuation with decreasing thickness near cutoff is greater than therate related to the ss_(b) ⁰ mode in symmetric structures. However fieldconfinement also diminishes rapidly near cutoff, implying that thestructures ought to be fabricated to very tight tolerances and that allmetal-dielectric interfaces should be of the highest quality. It hasalso been found that decreasing the width of the film increases thecutoff thickness of the main long-ranging mode. Below this cutoffthickness, no purely bound long-ranging mode exists. The long-rangingmodes supported by metal films of finite-width are thus more sensitiveto the asymmetry in the structure as compared to the s_(b) modesupported by similar slab waveguides. This is a potentially usefulresult in that a small induced change in substrate or superstraterefractive index can have a greater impact on the long-ranging modesupported by a finite-width structure as compared to a similar slabwaveguide.

Parts of the foregoing theoretical discussion have been published by theinventor in references [13][20], [44] and [45].

SPECIFIC EMBODIMENTS AND EXAMPLES OF APPLICATION

Examples of practical waveguide structures, and integrated opticsdevices which can be implemented using the invention, will now bedescribed with reference also to FIGS. 27 to 42, 51 and 52. Unlessotherwise stated, where a waveguide structure is shown, it will have ageneral construction similar to that shown in FIGS. 1(a) and 1(b) orthat shown in FIGS. 17(a) and 17(b).

Waveguides, structures and devices disclosed herein operate withradiation:

having a wavelength such that a plasmon-polariton wave is supported;

at optical wavelengths;

at optical communications wavelengths;

at wavelengths in the range of 800 nm to 2 μm;

at wavelengths near 1550 nm;

at wavelengths near 1310 nm;

at wavelengths near 850 nm;

at wavelengths near 980 nm.

It should be appreciated that references to wavelength should beinterpreted as meaning the centre free space wavelength of the spectrumassociated with the input radiation.

The waveguide structure 100 shown in FIGS. 1(a) and 1(b) comprises astrip of finite thickness t and width w of a first material having ahigh free (or almost free) charge carrier density, surrounded by asecond material which has a very low free (or almost free) chargecarrier density. The strip material can be a metal or a highly dopedsemiconductor and the background material can be a dielectric, or anundoped or low doped semiconductor. The thickness t and the width w ofthe strip are selected such that the waveguide supports the mainlong-ranging plasmon-polariton mode of interest, the ss_(b) ⁰ mode, atthe free-space wavelength of interest.

The waveguides will propagate plasmon-polariton waves if the strip has awidth in the range from about 0.1 μm to about 12 μm and a thickness inthe range from about 5 nm to about 100 nm, particular dimensionsdepending on the index of refraction of the surrounding material, thestrip material and the free-space wavelength of operation.

FIGS. 51 and 52 give the mode power attenuation for example waveguidesconstructed from strips of gold (Au) and aluminium (Al), respectively,each embedded in silicon dioxide (SiO₂), for various widths andthicknesses of the metal strip. The analyses were carried out at anoptical free space wavelength of 1550 nm. The curves show that very lowattenuation values can be obtained with metal strips of practicaldimensions. Generally, the attenuation using the gold strip is about onehalf of that obtained with the aluminium strip having similardimensions. Suitable ranges for the dimensions of the strip, in theseparticular waveguide examples, can be deduced from FIGS. 51 and 52. Asuitable range for the thickness of the strip is from about 5 nm toabout 50 nm, and a suitable range for the width of the strip is fromabout 0.5 μm to about 12 μm. For either of these metals, particularlygood dimensions are a thickness of about 20 nm and a width of about 4μm; such a strip yields a low loss waveguide having a mode size of about10 μm.

For a waveguide structure having particular materials for the strip andsurrounding material, operable at a particular wavelength, there will bea range of thickness and width for the strip which will allow theplasmon-polariton wave to be supported. For metallic strips surroundedby material such as silicon dioxide, silicon oxynitride or siliconnitride, having a refractive index in the range from about 1.4 to about2.0, the range of dimensions for the metallic strip is the width in therange from about 0.5 μm to about 12 μm and the thickness in the rangefrom about 5 nm to about 50 nm. Such waveguide structures supporteffectively the propagation of a plasmon-polariton wave having awavelength in the range from about 0.8 μm to about 2 μm. For operationin the wavelength range from about 1.3 μm to about 1.7 μm, gooddimensions for the metallic strip are a width in the range from about0.7 μm to about 8 μm and a thickness in the range from about 15 nm toabout 25 nm. A particularly good choice for the dimensions of themetallic strip is a width of about 4 μm and a thickness of about 20 nmfor operation at a wavelength near 1.55 μm. Other materials having anindex of refraction approximately in the same range require stripdimensions in approximately the same ranges.

For strips surrounded by materials such as lithium niobate or PLZT,having a refractive index in the range from about 2 to about 2.5, andrequired to support effectively the propagation of a plasmon-polaritonwave having a free space wavelength in the range from about 0.8 μm toabout 2 μm, the ranges of dimensions for the strip preferably include awidth in the range from about 0.15 μm to about 6 μm and a thickness inthe range from about 5 nm to about 80 nm. For operation in thewavelength range from about 1.3 μm to about 1.7 μm, good dimensions forthe strip are a width in the range from about 0.4 μm to about 2 μm andthickness in the range from about 15 nm to about 40 nm. For operation ata wavelength near 1.55 μm, the dimensions of the strip preferably are awidth of about 1 μm and a thickness of about 20 nm. Other surroundingmaterials having an index of refraction approximately in the same rangerequire strip dimensions in approximately the same ranges.

For strips surrounded by materials such as silicon, gallium arsenide,indium phosphide or other material having a refractive index in therange from about 2.5 to about 3.5, and required to support effectivelythe propagation of a plasmon-polariton wave having a free spacewavelength in the range from about 0.8 μm to about 2 μm, the ranges ofdimensions for the strip preferably include a width in the range fromabout 0.1 μm to about 2 μm and thickness in the range from about 5 nm toabout 30 nm. For operation in the wavelength range from about 1.3 μm toabout 1.7 μm, good dimensions for the strip are a width in the rangefrom about 0.13 μm to about 0.5 μm and thickness in the range from about10 nm to about 20 nm. For operation at a wavelength near 1.55 μm, thedimensions of the strip preferably are a width of about 0.25 μm andthickness of about 15 nm. Other surrounding materials having an index ofrefraction approximately in the same range require strip dimensions inapproximately the same ranges.

Unless otherwise stated, when waveguide structure dimensions arementioned from this point onward, they refer to the Au/SiO₂ materialcombination at an operating optical free-space wavelength of 1550 nm.

The plasmon-polariton wave which propagates along a waveguide structuremay be excited by an appropriate optical field incident at one of theends of the waveguide, as in an end-fire configuration, and/or bydifferent radiation coupling means. In order to achieve good couplingefficiency with the input and output means, the plasmon-polariton wavepreferably has a transverse electric field component that overlaps wellwith that of the fundamental mode of propagation supported by the inputand output means. Tapered input and output strip sections can be used tomatch the mode sizes of the plasmon-polariton waveguide and thewaveguide used as the input and output means, in order to achieve highcoupling efficiency. An example of an appropriate end-fire arrangementcomprises a standard optical fibre butt-coupled to the input of thewaveguide (the output of the waveguide can also be butt-coupled to afibre).

An example waveguide structure achieving high coupling efficiency withstandard optical fibre at a free space wavelength near 1.55 μm comprisesan Au strip surrounded by SiO₂, the strip having a thickness of about 20nm and a width in the range from about 4 μm to about 8 μm. Alternativemeans for exciting the waveguide include excitation at an intermediateposition using, for example, a prism and the so-called attenuated totalreflection method (ATR).

Suitable materials for the surrounding material include (but are notlimited to) glass, glasses, quartz, polymer, silicon dioxide, siliconnitride, silicon oxynitride, and undoped or very lightly doped GaAs, InPor Si. The material may comprise single crystal or partially crystallinematerial. The surrounding material may comprise electro-optic crystalsor material such as lithium niobate (LiNbO₃), PLZT or electro-opticpolymers. The surrounding material is not necessarily homogeneous.

Suitable materials for the strip include (but are not limited to)metals, semi-metals, and highly n- or p-doped semiconductors such asGaAs, InP or Si. Suitable metals for the strip may comprise, a singlemetal, or a combination of metals, selected from the group Au, Ag, Cu,Al, Pt, Pd, Ti, Ni, Mo, and Cr, preferred metals being Au, Ag, Cu, andAl. Metal silicides such as CoSi₂ are particularly suitable for use withSi as the surrounding material. A single material or combination ofmaterials which behave like metals, such as Indium Tin Oxide (ITO) canalso be used. In the context of this specification, the term “metallic”substances embraces such material(s). The metallic strip is notnecessarily homogeneous.

Particularly suitable combinations of materials include Au for the stripand SiO₂ for the surrounding material, or Au for the strip and LiNbO3for the surrounding material, or Al or CoSi₂ for the strip and Si forthe surrounding material, or Au for the strip and polymer for thesurrounding material, or gold for the strip and PLZT for the surroundingmaterial. These combinations are preferred because, in each case, thestrip material exhibits low optical absorption and is chemicallycompatible with the surrounding material. Devices may be fabricatedusing known deposition techniques or wafer bonding and polishing for thecladding materials, and known lithographic and deposition techniques forthe strip.

The waveguide structures may comprise: a strip that is homogeneous and asurrounding material that is homogeneous, a strip that is homogeneousand a surrounding material that is inhomogeneous; a strip that isinhomogeneous and a surrounding material that is homogeneous; or a stripthat is inhomogeneous and a surrounding material that is inhomogeneous.An inhomogeneous strip can be formed from a continuously variablematerial composition, or strips or laminae. An inhomogeneous surroundingmaterial can be formed from a continuously variable materialcomposition, or strips or laminae.

Generally, a plasmon-polariton waveguide having a metallic strip oflarge aspect ratio supports substantially TM polarized light, ie.: thetransverse electric field component of the plasmon-polariton wave, thess_(b) ⁰ mode, is aligned substantially with the normal to the largestdimension in the waveguide cross-section. Thus, a straight waveguide 100with the dimensions set out above is polarisation sensitive. Theplasmon-polariton wave is highly linearly polarised in the verticaldirection, i.e. perpendicular to the plane of the strip. Hence, it mayserve as a polarisation filter, whereby substantially only a verticalpolarised mode (aligned along the y-axis as defined in FIG. 1(a)) of theincident light is guided.

The length l shown in FIG. 1(b) is arbitrary and will be selected toimplement a desired interconnection.

FIG. 27 shows a transition waveguide section 102 having stepped sideswhich can be used to interconnect two sections of waveguide havingdifferent widths. The larger width can be used to more effectivelycouple the waveguide to input/output means, such as fibres. The reducedwidth helps to reduce the insertion loss of the waveguide. Preferredwidths are about W₂=8 μm to couple to single mode fibre and about W₁=4μm for the waveguide width. Any symmetry of the structure shown can beused.

FIG. 28 shows an angled section 104 which can be used as aninterconnect. Its dimensions, W₁, W₂ and 1 and the angles φ₁ and φ₂, areadjusted for a particular interconnection application as needed. Usuallythe angles are kept small, in the range of about 1 to about 15 degreesand the input and output widths are usually similar, about 4 μm.Although the sides of the angled section 104 shown in FIG. 28 aretapered, they could be parallel. It should also be appreciated that theangle of the inclination could be reversed, i.e. the device could besymmetrical about the bottom right hand corner shown in FIG. 28 ortransposed about that axis if not symmetrical about it.

FIG. 29 shows a tapered waveguide section 106, which can be used tointerconnect two waveguides of different widths. The length of the taperis usually adjusted such that the angles are small, preferably in therange from about 0.5 to about 15 degrees. The taper angles at the twosides are not necessarily the same. Such a configuration might be usedas an input port, perhaps as an alternative to the layout shown in FIG.27, or as part of another device, such as a power splitter. The largerwidth can be used to more effectively couple the waveguide toinput/output means, such as fibres. The reduced width helps to reducethe insertion loss of the waveguide. Typical widths are about W₂=8 μm tocouple to standard single mode fibre and about W₁=4 μm for the waveguidewidth. Any symmetry of the structure shown can be used.

FIG. 30 illustrates an alternative transition waveguide section 130which has curved sides, rather than straight as in the trapezoidaltransition section disclosed in FIG. 29. In FIG. 30, the curved sidesare shown as sections of circles of radius R₁ and R₂, subtending anglesφ₁ and φ₂ respectively, but it should be appreciated that variousfunctions can be implemented, such as exponential or parabolic, suchthat the input/output reflections and the transition losses areminimised.

FIG. 31 shows a curved waveguide section 108 which can be used toredirect the plasmon-polariton wave. The angle φ of the bend can be anyangle suitable for a particular implementation.

In addition to the width and thickness of the strip, critical dimensionsin the design of a bend include the bending radius R and offsets O₁ andO₂ determining the positions of the input and output straight sections100. Although the bend will work for many strip dimensions and benddesigns, i.e., the structure 108 will convey the plasmon-polariton wavearound the bend, there may be (i) radiation loss or leakage out of thebend, (ii) transition losses at the planes where the bent section meetsthe straight sections, and possibly also (iii) reflections back towardsthe direction from which the wave came. Minimal radiation loss orleakage is obtained by selecting a radius of curvature for the stripthat is greater than a threshold value, for which radiation isnegligible.

Reduced transition and reflection losses may be obtained by offsettingthe input and output waveguides 100 radically outwards relative to theends of the bend. The reason for this is that the straight waveguidesections 100 have an optical field extremum that peaks along thelongitudinal centre line of the strip, and decays towards its edges. Inthe bend, the extremum of the optical field distribution shifts towardsthe exterior of the bend. This results in increased radiation or leakagefrom the bend and increased transition and reflection losses due to amismatch in the field distributions. Offsetting the input and outputwaveguides 100 towards the outside of the bend aligns the extrema oftheir optical fields more closely with that of the optical field in thebent section 108, which helps to reduce, even minimise, both transitionand reflection losses. The smaller the radius R, the greater theradiation from the bend. Also the offsets O₁ and O₂ are related to theradius R. Optimum values for these parameters would have to bedetermined according to the specific bending requirements.

It should also be noted that it is not necessary to connect the inputand output waveguides 100 directly to the curved section. As shown inFIG. 31, it is possible to have a short spacing d₁ between the end ofthe input waveguide 100 and the adjacent end of the curved section 108.Generally speaking, that spacing d₁ should be minimised, even zero, andprobably no more than a few optical wavelengths. A similar offset O₂ andspacing d₂ could be provided between the bend 108 and the outputstraight waveguide 100.

Although FIG. 31 shows no gradual transition between the straightwaveguides 100 at the input and output and the ends of the curvedsection 108, it is envisaged that, in practice, a more gradual offsetcould be provided so as to reduce edge effects at the corners.

Estimates of radiation loss associated with 90° bends were obtained as afunction of the bend's radius of curvature R for various strip widthsand thickness waveguide bends comprised of a gold (Au) strip, and fortwo cases of surrounding material: silicon dioxide (SiO₂) and lithiumniobate (LiNbO3). The results clearly indicated the onset of significantradiation loss as the radius of curvature for a particular stripgeometry was reduced. It was inferred from the results that good bendingradii are in the range from about 100 μm to about 10 cm for a stripwidth in the range from about 0.1 μm to about 12 μm and a stripthickness in the range from about 5 nm to about 100 nm.

Acceptable 90 degree bends, comprising strips surrounded by materialssuch as silicon dioxide, silicon oxynitride or silicon nitride, having arefractive index in the range from about 1.4 to about 2.0, the range ofdimensions for the metallic strip being a width in the range from about0.5 μm to about 12 μm and a thickness in the range from about 5 nm toabout 50 nm should have a radius of curvature in the range from about100 μm to about 10 cm. Such bends support effectively the propagation ofa plasmon-polariton wave having a wavelength in the range from about 0.8μm to about 2 μm. For operation in the wavelength range from about 1.3μm to about 1.7 μm, 90 degree bends have the following dimensions forthe metallic strip: a width in the range from about 0.7 μm to about 8μm, a thickness in the range from about 15 nm to about 25 nm and aradius of curvature in the range from about 1 mm to about 10 cm. Foroperation at a wavelength near 1.55 μm, a particularly good choice for a90 degree bend is a metallic strip having a width of about 6 μm, athickness of about 20 nm and a radius of about 2 cm. Other materialshaving an index of refraction approximately in the same range requirestrip dimensions and radii of curvature in approximately the sameranges.

For 90 degree bends comprising strips surrounded by materials such aslithium niobate or PLZT, having a refractive index in the range fromabout 2 to about 2.5, required to support effectively the propagation ofa plasmon-polariton wave having a wavelength in the range from about 0.8μm to about 2 μm, the ranges of dimensions for the metallic stripinclude width in the range from about 0.15 μm to about 6 μm, thicknessin the range from about 5 nm to about 80 nm, and radius of curvature inthe range from about 100 μm to about 10 cm. For operation in thewavelength range from about 1.3 μm to about 1.7 μm, 90 degree bendspreferably have the following dimensions for the metallic strip: a widthin the range from about 0.4 μm to about 2 μm, a thickness in the rangefrom about 15 nm to about 40 nm and a radius of curvature in the rangefrom about 1 mm to about 10 cm. A particularly good choice for a 90degree bend is a metallic strip having a width of about 1.5 μm, athickness of about 20 nm and a radius of about 4 cm for operation at awavelength near 1.55 μm. Other materials having an index of refractionapproximately in the same range require strip dimensions and radii ofcurvature in approximately the same ranges. Similar ranges apply tosemiconductors having a refractive index in the range from about 2.5 toabout 3.5, such as silicon, gallium arsenide and indium phosphide.

The radius of curvature selected can be smaller than that used for a 90degree bend if the desired bending angle is smaller than 90 degrees.

FIG. 32 shows a two-way power splitter 110 formed from a trapezoidalsection 106 with a straight section 100 coupled to its narrower end 112and two angled sections 104 coupled side-by-side to its wider end 114.The distances between the input waveguide 100 and the narrower end 112of the tapered section 106, and between the output waveguides 104 andthe wider end 114 of the tapered section 106, d₁, d₂ and d₃,respectively, should be minimised. The angle between the outputwaveguides 104 can be in the range of 0.5 to 10 degrees and their widthsare usually similar. The offsets S₁ and S₂ between the output waveguidesand the longitudinal centre line of the trapezoidal section 106preferably are set to zero, but could be non-zero, if desired, and varyin size. Ideally, however, the output sections 104 should together beequal in width to the wider end 114.

Offset S₁ need not be equal to offset S₂ but it is preferable that bothare set to zero. The widths of the output sections 104 can be adjustedto vary the ratio of the output powers. The dimensions of the centretapered section 106 are usually adjusted to minimise input and outputreflections and radiation losses in the region between the outputsections 104.

It should also be noted that the centre tapered section 106 could haveangles that vary according to application and need not be symmetrical.

It is envisaged that the tapered section 106 could be replaced by arectangular transition section having a width broader than the width ofthe input waveguide 100 so that the transition section favouredmultimode propagation causing constructive and destructive interferencepatterns throughout its length. The length could be selected so that, atthe output end of the rectangular transition section, the constructiveportions of the interference pattern would be coupled into the differentwaveguides establishing, in effect, a 1-to-N power split. Such asplitter then would be termed a multimode interferometer-based powerdivider.

It should be appreciated that the device shown in FIG. 32 could also beused as a combiner. In this usage, the light would be injected into thewaveguide sections 104 and combined by the tapered centre section 106 toform the output wave which would emerge from the straight waveguidesection 100.

In either the Y splitter or the interferometer-based power divider, thenumber of arms or limbs 104 at the output could be far more than the twothat are shown in FIG. 32.

It is also feasible to have a plurality of input waveguides. This wouldenable an N×N divider to be constructed. The dimensions of thetransition section 106 then would be controlled according to the type ofsplitting/combining required.

As shown in FIG. 33(a), an angled waveguide section 104 may be used toform an intersection between two straight waveguide sections 100, withthe dimensions adjusted for the particular application. It should benoted that, as shown in FIG. 33(a), the two straight sections 100 areoffset laterally away from each other by the distances O₁ and O₂,respectively, which would be selected to optimise the couplings byreducing radiation, transition and reflection losses. The angle of thetrapezoidal section 104 relative to the sections 100 will be a factor indetermining the best values for the offsets O₁ and O₂. The sections 100and 104 need not be connected directly together, but could be spaced bythe distances d₁ and d₂ and/or coupled by a suitable transition piecethat would make the junction more gradual (i.e., the change of directionwould be more gradual).

The embodiments of FIGS. 31 and 33(a) illustrate a general principle ofaligning optical fields, conveniently by offsets, wherever there is atransition or change of direction of the optical wave and an inclinationrelative to the original path, which can cause radiation, transition andreflection losses if fields are misaligned. Such offsets could beapplied whether the direction-changing sections were straight or curved.

As shown in FIG. 33(b), an alternative embodiment to that shown in FIG.33(a) is obtained by replacing the angled section 104 by a pair ofconcatenated bend sections 108 arranged to form an S bend (with offsets)in order to provide the interconnection between the sections 100. Thebend sections could be replaced with bend sections having a continuouslyvariable radius of curvature implementing a bend profile other thancircular.

As illustrated in FIG. 34(a), a power divider 116 can also beimplemented using a pair of concatenated bend sections 108 instead ofeach of the angled sections 104 in the splitter 110 shown in FIG. 32. Asshown in FIG. 34(a), in each pair, the bend section nearest to the widerend 114 of the tapered section 106 bends outwards from the longitudinalcentre line of the tapered section 106 while the other section bendsoppositely so that they form an “S” bend. Also, the bend sections ineach pair are offset by distance O₁ or O₂ one relative to the other forthe reasons discussed with respect to the bend 108 shown in FIG. 31.Other observations made regarding the power divider and the bend sectiondisclosed in FIGS. 31 and 32 respectively, also apply to this case.

FIG. 34(b) shows a modification to the power divider of FIG. 34(a)specifically the use of a bifurcated transition section 106′ having anarrower end portion 115A and two curved sections 115B and 115Cdiverging away from the narrower end portion 115A; in effect, thetransition section comprising two mirrored and overlapping bendsections. The light emerges from respective distal ends of the curvedsections 115B and 115C. Two additional bend sections 108 are shownconnected to distal ends of the two curved sections 115B and 115C,respectively, in effect forming with the transition section 106′ twomirrored and overlapping S-bends.

FIG. 35 illustrates a Mach-Zender interferometer 118 created byinterconnecting two power splitters 110 as disclosed in FIG. 32. Ofcourse, either or both of them could be replaced by the power splitter116 shown in FIG. 34(a) or FIG. 34(b). Light injected into one of theports, i.e. the straight section 100 of one power splitter 110/116, issplit into equal amplitude and phase components that travel along theangled arms 104 of the splitter, are coupled by straight sections 100into the corresponding arms of the other splitter, and then arerecombined to form the output wave.

If the insertion phase along one or both arms of the device is modified,then destructive interference between the re-combined waves can beinduced. This induced destructive interference is the basis of a devicethat can be used to modulate the intensity of an input optical wave. Thelengths of the arms 100 are usually adjusted such that the phasedifference in the re-combined waves is 180 degrees for a particularrelative change in insertion phase per unit length along the arms. Thestructure will thus be optically long if the mechanism used to modifythe per unit length insertion phase is weak (or optically short if themechanism is strong).

FIG. 36(a) illustrates a modulator 120 based on the Mach-Zender 118disclosed in FIG. 35. As illustrated also in FIG. 36(b), parallel plateelectrodes 122 and 124 are disposed above and below, respectively, eachof the strips 100 which interconnects two angled sections 104, andspaced from it, by the dielectric material, at a distance large enoughthat optical coupling to the electrodes is negligible. The electrodesare connected in common to one terminal of a voltage source 126, and theintervening strip 100 is connected using a minimally invasive contact tothe other terminal. Variation of the voltage V applied by source 126effects the modulating action. According to the plasma model for thestrip 100, a change in the carrier density of the latter (due tocharging +2Q or −2Q) causes a change in its permittivity, which in turncauses a change in the insertion phase of the arm. (The change inducedin the permittivity is described by the plasma model representing theguiding strip 100 at the operating wavelength of interest. Such model iswell known to those of ordinary skill in the art and so will not bedescribed further herein. For more information the reader is directed toreference [21], for example.) This change is sufficient to inducedestructive interference when the waves in both arms re-combine at theoutput combiner.

FIG. 36(c) illustrates an alternative connection arrangement in whichthe two plate electrodes 122 and 124 are connected to respective ones ofthe terminals of the voltage source 126. In this case, the dielectricmaterial used as the background of the waveguide is electro-optic(LiNbO₃, a polymer, . . . ). In this instance, the applied voltage Veffects a change in the permittivity of the background dielectric, thuschanging the insertion phase along the arm. This change is sufficient toinduce destructive interference when the waves in both arms re-combineat the output combiner.

It will be noted that, in FIG. 36(a), one voltage source supplies thevoltage V₁ while the other supplies the voltage V₂. V₁ and V₂ may or maynot be equal.

For both cases described above, it is possible to apply voltages inopposite polarity to both arms of the structure. This effects anincrease in the insertion phase of one arm and a decrease in theinsertion phase of the other arm of the Mach-Zender (or vice versa),thus reducing the magnitude of the voltage or the length of thestructure required to achieve a desirable degree of destructiveinterference at the output.

Also, it is possible to provide electrodes 122 and 124 and a source 126for only one of the intervening strips 100 in order to provide therequired interference.

It should be appreciated that other electrode structures could be usedto apply the necessary voltages. For example, the electrodes 122 and 124could be coplanar with the intervening strip 100, one on each side ofit. By carefully laying out the electrodes as a microwave waveguide, ahigh frequency modulator (capable of modulation rates in excess of 10Gbit/s) can be achieved.

FIG. 37 illustrates an alternative implementation of a Mach-Zender 128which has the same set of waveguides as that shown in FIG. 35 but whichmakes use of magnetic fields B applied to either or both of the middlestraight section arms to induce a change in the permittivity tensordescribing the strips. (The change induced in the tensor is described bythe plasma model representing the guiding strip at the operatingwavelength of interest. Such model is well known to those of ordinaryskill in the art and so will not be described further herein. For moreinformation the reader is directed to reference [21], for example.) Thechange induced in the permittivity tensor will induce a change in theinsertion phase of either or both arms thus inducing a relative phasedifference between the light passing in the arms and generatingdestructive interference when the waves re-combine at the outputcombiner. Modulating the magnetic field thus modulates the intensity ofthe light transmitted through the device. The magnetic field B can bemade to originate from current-carrying wires or coils disposed aroundthe arms 100 in such a manner as to create the magnetic field in thedesired orientation and intensity in the optical waveguides. Themagnetic field may have one or all of the orientations shown, B_(x),B_(y) or B_(z) or their opposites. The wires or coils could befabricated using plated via holes and printed lines or other conductorsin known manner. Alternatively, the field could be provided by anexternal source, such as a solenoid or toroid having poles on one orboth sides of the strip.

FIG. 38 illustrates a periodic waveguide structure 132 comprising aseries of unit cells 134, where each cell 134 comprises two rectangularwaveguides 100 and 100′ having different lengths l₁ and l₂ and widths w₁and w₂, respectively. The dimensions of the waveguides in each unit cell134, the spacing d₁ therebetween, the number of unit cells, and thespacings d₂ between cells are adjusted such that reflection occurs at adesired operating wavelength or over a desired operating bandwidth foran optical signal propagating along the grating axis, i.e. thelongitudinal axis of the array of cells 134. The period of the periodicstructure, i.e. the length of each unit cell, l₁+l₂+d₁+d₂, can be madeoptically long, such that a long-period periodic structure is obtained.The dimensions of the elements 100, 100′ in each unit cell 134 can alsobe made to change along the direction of the periodic structure in orderto implement a prescribed transfer, function (like in a chirped periodicstructure).

It should be noted that the waveguides 100, 100′ in each cell need notbe rectangular, but a variety of other shapes could be used. Forexample, FIG. 39 illustrates a portion, specifically two unit cells 138only, of an alternative periodic structure 136 in which each unit cell138 comprises two of the trapezoidal waveguide sections 106, 106′ likethat described with reference to FIG. 30, with their wider edgesopposed.

As another alternative, the trapezoidal waveguides 106/106′ could bereplaced by the transition sections 130, shown in FIG. 30, with orwithout spacings d₁ and d₂, to form a periodic structure havingsinusoidally-varying sides. It should be noted that these periodicstructures are merely examples and not intended to provide an exhaustivedetailing of all possibilities; various other periodic structures couldbe formed from unit cells comprised of all sorts of different shapes andsizes of elements.

It should be noted that voltages can be applied to some or all of thestrips in order to establish charges on the strips of the unit cells,which would change their permittivity and thus vary the optical transferfunction of the periodic structures. If the dielectric materialsurrounding the strip is electro-optic, then the applied voltages wouldalso change the permittivity of the dielectric, which also contributesto changing of the optical transfer function of the periodic structure.

A two-dimensional photonic bandgap structure can be created by placingtwo or more of the periodic structures side-by-side to form atwo-dimensional array of unit cells (comprised of strips of variousshapes and sizes). A three-dimensional array can be created by stackinga plurality of such two-dimensional arrays in numerous planes separatedby dielectric material. The size and shape of the strips are determinedsuch that stop bands in the optical spectrum appear at desired spectrallocations.

FIG. 40(a) illustrates an edge coupler 139 created by placing two strips100″ parallel to each other and in close proximity over a certainlength. The separation S_(c) between the strips 100″ could be from about1 μm (or less) to about 20 μm and the coupling length L_(c) could be inthe range of a few microns to a few dozen millimeters depending on theseparation S_(c), width and thickness of the strips 100″, the materialsused, the operating wavelength, and the level of coupling desired. Sucha positioning of the strips 100″ is termed “edge coupling”. For example,if the strips are Au, the surrounding material is SiO₂ and the operatingfree space wavelength is near 1550 nm, good coupling lengths L_(c) arein the range from about 100 μm to about 5 mm and good separations S_(c)are in the range from about 2 μm to about 20 μm. Specific dimensionsdepend on the thickness and width of the strips and are selected toimplement a desired coupling factor.

The gaps between the input and output of the waveguide sections shownwould ideally be set to zero and a lateral offset provided betweensections where a change of direction is involved. As shown in FIG.40(c), concatenated bend sections 108 forming an S bend, as discussed inthe embodiments associated with FIGS. 33 and 34 could be used instead ofthe sections 104, 100 and 100″ shown in FIG. 40(a). Other observationsmade regarding the bend section disclosed in FIG. 31 also hold in thiscase.

Although only two strips 100″ are shown in the coupled section, itshould be understood that more than two strips can be coupled togetherto create an N×N coupler.

As illustrated in FIG. 40(b) a voltage can be applied to the twoedge-coupled sections 100″ via minimally invasive electrical contacts.FIG. 40(b) shows a voltage source 126 connected directly to the sections100″ but, if the sections 100, 104 and 100″ in each arm are connectedtogether electrically, the source 126 could be connected to one of theother sections in the same arm. Applying a voltage in such a mannercharges the arms of the coupler, which, according to the plasma modelfor the waveguide, changes its permittivity. If, in addition, thedielectric material placed between the two waveguides 100 iselectro-optic, then a change in the background permittivity will also beeffected as a result of the applied voltage. The first effect issufficient to change the coupling characteristics of the structure but,if an electro-optic dielectric is also used, as suggested, then botheffects will be present, allowing the coupling characteristics to bemodified by applying a lower voltage.

FIGS. 41(a) and 41(b) illustrate coupled waveguides similar to thoseshown in FIG. 40(a) but placed on separate layers in a substrate havingseveral layers 140/1, 140/2 and 140/3. The strips could be placed onedirectly above the other with a thin region of dielectric of thickness dplaced between them. Such positioning of the strips is termed “broadsidecoupling”. The coupled guides can also be offset from broadside adistance S_(c), as shown in FIGS. 41(a) and 41(b). The strips could beseparated by about d=1 μm (or less) to about 20 μm, the coupling lengthcould be in the range of a few microns to a few dozens millimeters andthe separation S_(c) could be in the range of about −20 to about +20 μm,depending on the width and thickness of the strips, the materials usedand the level of coupling desired. (The negative indicates an overlapcondition).

As before, curved sections could be used instead of the straight andangled sections shown in FIG. 41(a).

Gaps can be introduced longitudinally between the segments of strip ifdesired and a lateral offset between the straight and angled (or curved)sections could be introduced.

Though only two strips are shown in the coupled section, it should beunderstood that a plurality of strips can be coupled together on a layerand/or over many layers to create an N×N coupler.

As shown in FIG. 41(b), a voltage source 126 could be connected directlyor indirectly to the middle (coupled) sections 100″ in a similar mannerto that shown in FIG. 40(b).

It should be appreciated that in any of the couplers described withreference to FIGS. 40(a), 40(c) and 41(a), the adjusting means shown inFIG. 40(b) could be replaced by either of the electrode configurationsand biasing arrangements described with reference to FIGS. 36(b) and36(c). It should also be noted that the electrode configuration andbiasing arrangement could be applied to either or both of strips 100″ ofsuch couplers.

As illustrated in FIG. 42, an intersection 142 can be created byconnecting together respective ends of four of the angled waveguidesections 104, their distal ends providing input and output ports for thedevice. When light is applied to one of the ports, a prescribed ratio ofoptical power emerges from the output ports at the opposite side of theintersection. The angles φ₁ . . . φ₄ can be set such that optical powerinput into one of the ports emerges from the port directly opposite,with negligible power transmitted out of the other ports. Any symmetryof the structure shown is appropriate.

Various other modifications and substitutions are possible withoutdeparting from the scope of the present invention. For example, althoughthe waveguide structure shown in FIGS. 1(a) and 1(b), and implicitlythose shown in other Figures, have a single homogeneous dielectricsurrounding a thin metal film, it would be possible to sandwich themetal film between two slabs of different dielectric material; or at thejunction between four slabs of different dielectric material. Moreover,the multilayer dielectric material(s) illustrated in FIG. 41(a) could beused for other devices too. Also, the thin metal film could be replacedby some other conductive material or a highly n- or p-dopedsemiconductor. It is also envisaged that the conductive film, whethermetal or other material, could be multi-layered.

Specific Embodiments of Modulation and Switching Devices

Modulation and switching devices will now be described which make use ofthe fact that an asymmetry induced in optical waveguiding structureshaving as a guiding element a thin narrow metal film may inhibitpropagation of the main long-ranging purely bound plasmon-polariton modesupported.

The asymmetry in the structure can be in the dielectrics surrounding themetal film. In this case the permittivity, permeability or thedimensions of the dielectrics surrounding the strip can be different. Anoteworthy case is where the dielectrics above and below the metal striphave different permittivities, in a manner similar to that shown in FIG.17(a).

A dielectric material exhibiting an electro-optic, magneto-optic,thermo-optic, or piezo-optic effect can be used as the surroundingdielectric medium. The modulation and switching devices make use of anexternal stimulus to induce or enhance the asymmetry in the dielectricsof the structure.

FIGS. 43(a) and 43(b) depict an electro-optic modulator comprising twometal strips 110 and 112 surrounded by a dielectric 114 exhibiting anelectro-optic effect. Such a dielectric has a permittivity that varieswith the strength of an applied electric field. The effect can be firstorder in the electric field, in which case it is termed the Pockelseffect, or second order in the electric field (Kerr effect), or higherorder. FIG. 43(a) shows the structure in cross-sectional view and FIG.43(b) shows the structure in top view. The lower metal strip 110 and thesurrounding dielectric 114 form the optical waveguide. The lower metalstrip 110 is dimensioned such that a purely bound long-rangingplasmon-polariton wave is guided by the structure at the opticalwavelength of interest. Since the “guiding” lower metal strip 110comprises a metal, it is also used as an electrode and is connected to avoltage source 116 via a minimally invasive electrical contact 118 asshown. The second metal strip 112 is positioned above the lower metalstrip 110 at a distance large enough that optical coupling between thestrips is negligible. It is noted that the second strip also be placedbelow the waveguiding strip instead of above. The second strip acts as asecond electrode.

The intensity of the optical signal output from the waveguide can bevaried or modulated by varying the intensity of the voltage V applied bythe source 116. When no voltage is applied, the waveguiding structure issymmetrical and supports a plasmon-polariton wave. When a voltage isapplied, an asymmetry in the waveguiding structure is induced via theelectro-optic effect present in the dielectric 114, and the propagationof the plasmon-polariton wave is inhibited. The degree of asymmetryinduced may be large enough to completely cut-off the main purely boundlong-ranging mode, thus enabling a very high modulation depth to beachieved. By carefully laying out the electrodes as a microwavewaveguide, a high frequency modulator (capable of modulation rates inexcess of 10 G bit/s) can be achieved.

FIGS. 44(a) and 44(b) show an alternative design for an electro-opticmodulator which is similar to that shown in FIG. 43(a) but compriseselectrodes 112A and 112B placed above and below, respectively, the metalfilm 110 of the optical waveguide at such a distance that opticalcoupling between the strips is negligible. FIG. 44(a) shows thestructure in cross-sectional view and FIG. 44(b) shows the structure intop view. A first voltage source 116A connected to the metal film 110and the upper electrode 112A applies a first voltage V₁ between them. Asecond voltage source 116B connected to metal film 110 and lowerelectrode 112B applies a voltage V₂ between them. The voltages V₁ andV₂, which are variable, produce electric fields E₁ and E₂ in portions114A and 114B of the dielectric material. The dielectric material usedexhibits an electro-optic effect. The waveguide structure shown in FIG.44(c) is similar in construction to that shown in FIG. 44(a) but onlyone voltage source 116C is used. The positive terminal (+) of thevoltage source 116C is shown connected to metal film 110 while itsnegative terminal (−) is shown connected to both the upper electrode112A and the lower electrode 112B. With this configuration, the electricfields E₁ and E₂ produced in the dielectric portions 114A and 114B,respectively, are in opposite directions. Thus, whereas, in thewaveguide structure of FIG. 44(a), selecting appropriate values for thevoltages V₁ and V₂ induces the desired asymmetry in the waveguidestructure of FIG. 44(c), the asymmetry is induced by the relativedirection of the electric field above and below the waveguiding strip110, since the voltage V applied to the electrodes 112A and 112Bproduces electric fields acting in opposite directions in the portions114A and 114B of the dielectric material.

The structures shown in FIGS. 44(a), (b) and (c) can operate to veryhigh frequencies since a microwave transmission line (a stripline) is ineffect created by the three metals.

FIG. 45 shows in cross-sectional view yet another design for anelectro-optic modulator. In this case, the metal film 110 is embedded inthe middle of dielectric material 114 with first portion 114D above itand second portion 114E below it. Electrodes 112D and 112E are placedopposite lateral along opposite lateral edges, respectively, of theupper portion 114D of the dielectric 114 as shown and connected tovoltage source 116E which applies a voltage between them to induce thedesired asymmetry in the structure. Alternatively, the electrodes 112D,112E could be placed laterally along the bottom portion 114E of thedielectric 114, the distinct portions of the dielectric material stillproviding the asymmetry being above and below the strip.

FIG. 46 shows an example of a magneto-optic modulator wherein thewaveguiding strip 110 and overlying electrode 112F are used to carry acurrent I in the opposite directions shown. The dielectric materialsurrounding the metal waveguide strip 110 exhibits a magneto-opticeffect or is a ferrite. The magnetic fields generated by the current Iadd in the dielectric portion between the electrodes 110 and 112F andessentially cancel in the portions above the top electrode 112F andbelow the waveguide 110. The applied magnetic field thus induces thedesired asymmetry in the waveguiding structure. The electrode 112F isplaced far enough from the guiding strip 110 that optical couplingbetween the strips is negligible.

FIG. 47 depicts a thermo-optic modulator wherein the waveguiding strip110 and the overlying electrode 112G are maintained at temperatures T₂and T₁ respectively. The dielectric material 114 surrounding the metalwaveguide exhibits a thermo-optic effect. The temperature differencecreates a thermal gradient in the dielectric portion 114G between theelectrode 112G and the strip 110. The variation in the appliedtemperature thus induce the desired asymmetry in the waveguidingstructure. The electrode 112G is placed far enough from the guidingstrip 110 that optical coupling between the strips is negligible.

It should be appreciated that the modulator devices described above withreference to FIGS. 43(a) to 47 may also serve as variable opticalattenuators with the attenuation being controlled via the externalstimulus, i.e. voltage, current, temperature, which varies theelectromagnetic property.

FIGS. 48, 49 and 50 depict optical switches that operate on theprinciple of “split and attenuate”. In each case, the input opticalsignal is first split into N outputs using a power divider; a one-to-twopower split being shown in FIGS. 48, 49 and 50. The undesired outputsare then “switched off” or highly attenuated by inducing a largeasymmetry in the corresponding output waveguides. The asymmetry must belarge enough to completely cut-off the main purely bound long-rangingmode supported by the waveguides. The asymmetry is induced by means ofoverlying electrodes as in the waveguide structures of FIGS. 43, 46 or47, respectively.

In the switches shown in FIGS. 48, 49 and 50, the basic waveguideconfiguration is the same and comprises an input waveguide section 120coupled to two parallel branch sections 122A and 122B by a wedge-shapedsplitter 124. All four sections 120, 122A, 122B and 124 are co-planarand embedded in dielectric material 126. The thickness of the metal filmis d₃. Two rectangular electrodes 128A and 128B, each of thickness d₁,are disposed above branch sections 122A and 122B, respectively, andspaced from them by a thickness d₂ of the dielectric material 126 at adistance large enough that optical coupling between the strips isnegligible. Each of the electrodes 128A and 128B is wider and shorterthan the underlying metal film 122A or 122B, respectively. In the switchshown in FIG. 48, the asymmetry is induced electro-optically by means ofa first voltage source 130A connected between metal film 122A andelectrode 128A for applying voltage V₁ therebetween, and a secondvoltage source 130B connected between metal film 122B and electrode128B, for applying a second voltage V₂ therebetween. In the switch shownin FIG. 49, the asymmetry is induced magneto-optically by a firstcurrent source 132A connected between metal film 122A and electrode128A, which are connected together by connector 134A to complete thecircuit, and a second current source 132B connected between metal film122B and electrode 128B, which are connected together by connector 134Bto complete that circuit.

In the switch shown in FIG. 50, the asymmetry is inducedthermo-optically by maintaining the metal strips 122A and 122B attemperature T₀ and the overlying electrodes 128A and 128B attemperatures T₁ and T₂, respectively.

It will be appreciated that, in the structures shown in FIGS. 48, 49 and50, the dielectric surrounding the metal strip will be electro-optic,magneto-optic, or thermo-optic, or a magnetic material such as aferrite, as appropriate.

In general, any of the sources, whether of voltage, current ortemperature, may be variable.

Although the switches shown in FIGS. 48, 49 and 50 are 1×2 switches, theinvention embraces 1×N switches which can be created by adding morebranch sections and associated electrodes, etc.

It will be appreciated that, where the surrounding material isacousto-optic, the external stimulus used to induce or enhance theasymmetry could be determined by analogy. For example, a structuresimilar to that shown in FIG. 45 could be used with the electro-opticmaterial replaced by acousto-optic material and the electrodes 112D and112E used to apply compression or tension to the upper portion 114D.

To facilitate description, the various devices embodying the inventionhave been shown and described as comprising several separate sections ofthe novel waveguide structure. While it would be feasible to constructdevices in this way, in practice, the devices are likely to comprisecontinuous strips of metal or other high charge carrier densitymaterial, i.e. integral strip sections, fabricated on the samesubstrate.

The foregoing examples are not meant to be an exhaustive listing of allthat is possible but rather to demonstrate the breadth of application ofthe invention. The inventive concept can be applied to various otherelements suitable for integrated optics devices. It is also envisagedthat waveguide structures embodying the invention could be applied tomultiplexers and demultiplexers.

Although embodiments of the invention have been described andillustrated in detail, it is to be clearly understood that the same isby way of illustration and example only and not to be taken by way oflimitation, the spirit and scope of the present invention being limitedonly by the appended claims.

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What is claimed is:
 1. An optical device comprising a waveguidestructure formed by a thin strip of material having a relatively highfree charge carrier density surrounded by material having a relativelylow free charge carrier density, the strip having finite width andthickness with dimensions such that optical radiation having a freespace wavelength in the range from about 0.8 μm to about 2 μm couples tothe strip and propagates along the length of the strip as aplasmon-polariton wave.
 2. A device according to claim 1, wherein thestrip is straight, curved, bent, or tapered.
 3. A device according toclaim 1, further comprising at least a second said waveguide structuresimilar to the first-mentioned waveguide structure, the second waveguidestructure comprising a second said strip having one end coupled to thefirst-mentioned strip, wherein the first-mentioned strip is curved andthe second strip is offset outwardly relative to an axis of curvature ofthe first-mentioned strip.
 4. A device according to claim 3, wherein thesecond strip is curved oppositely to the first strip such that the firstand second strips form an S-bend.
 5. A device according to claim 4,further comprising third and fourth said waveguide structures comprisingthird and fourth strips, respectively, the third strip having one endcoupled to an end of the first strip opposite that connected to thesecond strip and the fourth strip having one end coupled to an end ofthe second strip opposite that connected to the first strip, the thirdand fourth strips each being offset outwardly relative to an axis ofcurvature of the strip to which it is coupled.
 6. A device according toclaim 1, further comprising at least two additional said waveguidestructures comprising second and third strips, respectively, the secondstrip for inputting said radiation to one end of said first-mentionedstrip and the third strip for receiving said radiation from the oppositeend of said first-mentioned strip, wherein the first-mentioned strip iscurved and said second and third strips are each offset outwardlyrelative to an axis of curvature of the first-mentioned strip.
 7. Adevice according to claim 1, further comprising at least second andthird waveguide structures both similar in construction to thefirst-mentioned waveguide structure and having second and third strips,respectively, the second and third strips having respective ends coupledin common to one end of the strip of the first-mentioned waveguidestructure to form respective arms of a combiner/splitter, thearrangement being such that said optical radiation leaving saidfirst-mentioned strip via said one end will be split between said secondand third strips and conversely said optical radiation coupled to saidone end by said second and third strips will be combined to leave saidfirst-mentioned strip by an opposite end.
 8. A device according to claim7, further comprising a transition waveguide structure coupling thesecond and third strips to the first-mentioned strip, the transitionwaveguide structure being similar in construction to the first-mentionedwaveguide structure and comprising a strip having a narrower end coupledto the first-mentioned strip and a wider end, the second and thirdstrips being coupled together to the wider end.
 9. A device according toclaim 8, wherein the second and third strips each comprise an S-bend,and the S-bends diverge away from the wider end of the transition strip.10. A device according to claim 1, further comprising a bifurcatedtransition section (106′) having a narrower end portion (115A) coupledto the first-mentioned waveguide structure and two curved sections(115B, 115C) diverging away from the narrower end portion 115A to formrespective arms of a combiner/splitter, such that light entering thenarrower end portion will emerge from respective distal ends of thecurved sections 115B and 115C.
 11. A device according to claim 10,further comprising two additional bend sections (108) connected todistal ends of the curved sections (115B, 115C), respectively, to formwith the transition section two mirrored and overlapping S-bends.
 12. Adevice according to any one of claims 7 to 11, further comprising asecond combiner/splitter similar in construction to the firstcombiner/splitter and connected to the first combiner/splitter to form aMach-Zender interferometer, each arm of the first combiner/splitterbeing connected to a respective one of the arms of the secondcombiner/splitter to form a corresponding interferometer arm, thearrangement being such that optical radiation input via said first stripof the first combiner/splitter produces two plasmon-polariton waveportions which propagate along, respectively, arms of the Mach-Zenderinterferometer and are recombined by the second combiner/splitter.
 13. Adevice according to claim 12, wherein each arm of the firstcombiner/splitter is connected to a respective arm of the secondcombiner/splitter by a respective intermediate section of waveguidestructure similar in construction to the first waveguide structure, andthe device further comprises means for adjusting the characteristics ofone of said intermediate sections relative to those of the otherintermediate section and thereby propagation characteristics of thecorresponding one of said two plasmon-polariton wave portions so as toobtain destructive interference upon recombination and thereby modulatethe intensity of said optical radiation.
 14. A device according to claim13, wherein the material surrounding the strip of the waveguidestructure whose characteristics are adjusted is electro-optic, and theadjusting means establishes an electric field in said electro-opticmaterial and varies said electric field so as to vary the refractiveindex of the electro-optic material.
 15. A device according to claim 14,wherein the adjusting means comprises a pair of electrodes spaced apartwith the strip between them and a voltage source connected to theelectrodes for applying a voltage between the electrodes so as toestablish said electric field in said electro-optical material.
 16. Adevice according to claim 14, wherein the adjusting means comprises atleast one electrode adjacent the strip of the waveguide structure whosecharacteristics are adjusted and a voltage source for applying saidvoltage between the electrode and said strip so as to establish saidelectric field in said material therebetween.
 17. A device according toclaim 14, wherein the adjusting means comprises a pair of electrodesspaced apart with said strip therebetween and a voltage source connectedbetween said strip and both electrodes, in common, for applying avoltage between the electrodes and the strip to establish said electricfield in said electro-optic material.
 18. A device according to claim13, wherein the adjusting means is arranged to induce a magnetic fieldin said at least one of the parallel branches.
 19. A device according toclaim 13, wherein the adjusting means modulates the intensity of saidoptical radiation substantially to extinction.
 20. A device according toclaim 1, further comprising at least two additional waveguidestructures, the at least three waveguide structures arranged to form anintersection, respective strips of the at least three waveguidestructures each having one end connected to juxtaposed ends of the otherstrips to form said intersection, distal ends of the at least threestrips constituting ports such that optical radiation input via thedistal end of one of the strips will be conveyed across the intersectionto emerge from at least one of the other strips.
 21. A device accordingto any one of claims 3 to 20, wherein said strips are integral with eachother.
 22. A device according to claim 1, further comprising at least asecond waveguide structure similar in construction to thefirst-mentioned waveguide structure, the first and second waveguidestructures being arranged to form a coupler, first and second strips ofthe first and second waveguide structures, respectively, extendingparallel to each other and in close proximity such that propagation ofsaid optical radiation is supported by both strips, the device furthercomprising input means for inputting said optical radiation to at leastsaid first strip and output means for receiving at least a portion ofsaid optical radiation from at least said second strip.
 23. A deviceaccording to claim 22, wherein the first and second strips are notcoplanar.
 24. A device according to claim 22 or 23, further comprisingmeans for adjusting the characteristics of at least one of the first andsecond waveguide structures and thereby propagation characteristics ofsaid plasmon-polariton wave propagating along the coupled strips so asto control the degree of coupling between the strips.
 25. A deviceaccording to claim 22 or 23, wherein the material between the coupledstrips is electro-optic and further comprising adjusting means forestablishing an electric field in said electro-optic material andvarying said electric field so as to vary the refractive index of theelectro-optic material between the strips.
 26. A device according toclaim 25, wherein the adjusting means comprises a voltage sourceconnected to the coupled strips for applying a voltage between thestrips so as to establish said electric field in the said electro-opticmaterial.
 27. A device according to claim 25, wherein the adjustingmeans comprises at least one electrode adjacent at least one of thecoupled strips and a voltage source for applying a voltage between theelectrode and at least one of the coupled strips so as to establish saidelectric field in said material therebetween.
 28. A device according toclaim 22 or 23, wherein the material surrounding at least one of thecoupled strips is electro-optic and the adjusting means comprises a pairof electrodes spaced apart with said at least one of the coupled stripsbetween them and a voltage source connected to the electrodes forapplying a voltage between the electrodes so as to establish an electricfield in said electro-optic material, variation of said voltage causinga corresponding variation in the refractive index of said electro-opticmaterial.
 29. A device according to claim 22 or 23, wherein the materialsurrounding at least one of the strips is electro-optic, and theadjusting means comprises a pair of electrodes spaced apart with said atleast one of the coupled strips therebetween and a voltage sourceconnected between said at least one of the strip and both electrodes incommon, for applying a voltage between the electrodes and said at leastone of the strips to establish an electric field in said electro-opticmaterial, variation of said voltage causing a corresponding variation inthe reflective index of said electro-optic material.
 30. A deviceaccording to any one of claims 22 to 29, wherein the input means and theoutput means each comprise a pair of waveguide structures similar inconstruction to the first waveguide structure, and each pair comprises apair of strips connected at one end to the respective ends of thecoupled strips and diverging away therefrom so that distal ends of eachpair of strips are spaced apart by a distance significantly greater thanthe spacing between the coupled strips.
 31. A device according to claim30, wherein each of said diverging strips comprises an S-bend.
 32. Adevice according to claim 1, wherein the surrounding material isinhomogeneous.
 33. A device according to claim 32, wherein thesurrounding material comprises a continuously variable materialcomposition or a combination of slabs and/or strips and/or laminae. 34.A device according to claim 1, wherein said relatively low free chargecarrier density is substantially negligible.
 35. A device according toclaim 32, wherein the surrounding material comprises a single materialor a combination of materials selected from the group consisting ofglasses, electro-optic crystals, electro-optic polymers, and undoped orvery lightly doped semiconductors, and preferably selected from thegroup consisting of silicon dioxide, silicon nitride, siliconoxynitride, quartz, lithium niobate, lead lanthanum zirconium titanate(PLZT), gallium arsenide, indium phosphide and silicon.
 36. A deviceaccording to claim 1 or 32, wherein the strip is inhomogeneous.
 37. Adevice according to claim 36, wherein the strip material comprises asingle material or a combination of materials selected from the groupconsisting of metals, semi-metals, and highly n- or p-dopedsemiconductors, preferred materials being selected from the groupconsisting of gold, silver, copper, aluminium, platinum, palladium,titanium, nickel, molybdenum and chromium, metal silicides and highly n-or p-doped gallium arsenide (GaAs), indium phosphide (InP) or silicon(Si), and preferably from the subgroup consisting of gold (Au), silver(Ag), copper (Cu), and aluminium (Al), metal suicides such as cobaltdisilicide (CoSi₂), and materials which behave like metals, such asIndium Tin Oxide (ITO).
 38. An optical device according to claim 37,wherein the strip comprises layers of different ones of said materials.39. A device according to claim 38, wherein the strip comprises a layerof gold and a layer of titanium and is surrounded by silicon dioxide.40. A device according to claim 37, wherein the strip comprises gold andis surrounded by silicon dioxide.
 41. A device according to claim 37,wherein the strip comprises gold and is surrounded by lithium niobate.42. A device according to claim 37 wherein the strip comprises gold andis surrounded by PLZT.
 43. A device according to claim 37, wherein thestrip comprises gold and is surrounded by polymer.
 44. A deviceaccording to claim 37, wherein the strip comprises aluminium and issurrounded by silicon.
 45. A device according to claim 37, wherein thestrip comprises cobalt disilicide and is surrounded by silicon.
 46. Adevice according to claim 1, wherein the width is in the range fromabout 0.1 microns to about 12 microns and the thickness is in the rangefrom about 5 nm to about 100 nm.
 47. A device according to claim 46,wherein the surrounding material comprises silicon dioxide, siliconoxynitride, silicon nitride or other material having a refractive indexin the range from about 1.4 to about 2.0, the width of the strip is inthe range from about 0.5 μm to about 12 μm and the thickness of thestrip is in the range from about 5 nm to about 50 nm.
 48. A deviceaccording to claim 47, wherein the width of the strip is in the rangefrom about 0.7 μm to about 8 μm and the thickness of the strip is in therange from about 15 nm to about 25 nm, the device supporting propagationof a plasmon-polariton wave having a wavelength in the range from about1.3 μm to about 1.7 μm.
 49. A device according to claim 48, wherein thewidth is about 4 μm and the thickness is about 20 nm, the devicesupporting propagation of a plasmon-polariton wave having a wavelengthnear 1.55 μm.
 50. A device according to claim 46, wherein thesurrounding material comprises lithium niobate, PLZT or other materialhaving refractive index in the range from about 2 to about 2.5, thewidth of the strip being in the range from about 0.15 μm to about 6 μmand the thickness of the strip being in the range from about 5 nm toabout 80 nm.
 51. A device according to claim 50, wherein the width ofthe strip is in the range from about 0.4 μm to about 2 μm and thethickness of the strip is in the range from about 15 nm to about 40 nm,the device supporting propagation of a plasmon-polariton wave having awavelength in the range from about 1.3 μm to about 1.7 μm.
 52. A deviceaccording to claim 51, wherein the width of the strip is about 1 μm andthe thickness of the strip is about 20 nm, the device supportingpropagation of a plasmon-polariton wave having a wavelength near 1.55μm.
 53. A device according to claim 46, wherein the surrounding materialcomprises silicon, gallium arsenide, indium phosphide or other materialhaving a refractive index in the range from about 2.5 to about 3.5, thewidth of the strip being in the range from about 0.1 μm to about 2 μmand the thickness of the strip being in the range from about 5 nm toabout 30 nm.
 54. A device according to claim 53, wherein the width ofthe strip is in the range from about 0.13 μm to about 0.5 μm and thethickness of the strip is in the range from about 10 nm to about 20 nm,the device supporting propagation of a plasmon-polariton wave having awavelength in the range from about 1.3 μm to about 1.7 μm.
 55. A deviceaccording to claim 54, wherein the width of the strip is about 0.25 μmand the thickness of the strip is about 15 nm, the device supportingpropagation of a plasmon-polariton wave having a wavelength near 1.55μm.
 56. A device according to claim 2, wherein the strip is curved, itswidth is in the range from about 0.1 microns to about 12 microns, itsthickness is in the range from about 5 nm to about 100 nm, and itsradius of curvature is in the range from about 100 microns to about 10cm.
 57. A device according to claim 56, wherein the surrounding materialcomprises silicon dioxide, silicon oxynitride, silicon nitride, or othermaterial having a refractive index in the range from about 1.4 to about2.0, the width of the strip is in the range from about 0.5 μm to about12 μm and the thickness of the strip is in the range from about 5 nm toabout 50 nm the strip being curved with a radius of curvature in therange from about 100 μm to about 10 cm.
 58. A device according to claim57, wherein the width of the strip is in the range from about 0.7 μm toabout 8 μm, the thickness of the strip is in the range from about 15 nmto about 25 nm, and the radius of curvature is in the range from about 1mm to about 10 cm, the device supporting propagation of aplasmon-polariton wave having a wavelength in the range from about 1.3μm to about 1.7 μm.
 59. A device according to claim 58, wherein thewidth is about 6 μm, the thickness is about 20 nm, and the radius ofcurvature is about 2 cm, the device supporting propagation of aplasmon-polariton wave having a wavelength near 1.55 μm.
 60. A deviceaccording to claim 59, wherein the surrounding material compriseslithium niobate, PLZT, gallium arsenide, indium phosphide, silicon orother material having a refractive index in the range from about 2 toabout 3.5, the width of the strip being in the range from about 0.15 μmto about 6 μm and the thickness of the strip being in the range fromabout 5 nm to about 80 nm, the strip being curved with a radius ofcurvature in the range from about 100 μm to about 10 cm.
 61. A deviceaccording to claim 60, wherein the width of the strip is in the rangefrom about 0.4 μm to about 2 μm, the thickness is in the range fromabout 15 nm to about 40 nm, and the radius of curvature is in the rangefrom about 1 mm to about 10 cm, the device supporting propagation of aplasmon-polariton wave having a wavelength in the range from about 1.3μm to about 1.7 μm.
 62. A device according to claim 61, wherein thewidth of the strip is about 1.5 μm, the thickness of the strip is about20 nm, and the radius of curvature of the strip is about 4 cm, thedevice supporting propagation of a plasmon-polariton wave having awavelength near 1.55 μm.